# Posts Tagged upper bound

## Recent Postings from upper bound

### An Upper Bound on Neutron Star Masses from Models of Short Gamma-ray Bursts

The discovery of two neutron stars with gravitational masses $\approx 2~M_\odot$ has placed a strong lower limit on the maximum mass of a slowly rotating neutron star, and with it a strong constraint on the properties of cold matter beyond nuclear density. Current upper mass limits are much looser. Here we note that, if most short gamma-ray bursts are produced by the coalescence of two neutron stars, and if the merger remnant collapses quickly, then the upper mass limit is constrained tightly. We find that if the rotation of the merger remnant is limited only by mass-shedding (which seems plausible based on current numerical studies), then the maximum gravitational mass of a slowly rotating neutron star is between $\approx 2~M_\odot$ and $\approx 2.2~M_\odot$ if the masses of neutron stars that coalesce to produce gamma-ray bursts are in the range seen in Galactic double neutron star systems. These limits are increased by $\sim 4$% if the rotation is slowed by $\sim 30$%, and by $\sim 15$% if the merger remnants do not rotate at all. Future coincident detection of short gamma-ray bursts with gravitational waves will strengthen these arguments because they will produce tight bounds on the masses of the components for individual events. If these limits are accurate then a reasonable fraction of double neutron star mergers might not produce gamma-ray bursts. In that case, or in the case that many short bursts are produced instead by the mergers of neutron stars with black holes, the implied rate of gravitational wave detections will be increased.

### Lyth bound revisited [Cross-Listing]

Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.

### Lyth bound revisited [Cross-Listing]

Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.

### Lyth bound revisited [Replacement]

Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.

### Lyth bound revisited [Replacement]

Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.

### Lyth bound revisited [Replacement]

Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.

### Lyth bound revisited [Replacement]

Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.

### Lyth bound revisited

Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.

### Maximum mass of a barotropic spherical star [Cross-Listing]

The ratio of total mass $M$ to surface radius $R$ of spherical perfect fluid ball has an upper bound, $M/R < B$. Buchdahl obtained $B = 4/9$ under the assumptions; non-increasing mass density in outward direction, and barotropic equation of states. Barraco and Hamity decreased the Buchdahl’s bound to a lower value $B = 3/8$ $(< 4/9)$ by adding the dominant energy condition to Buchdahl’s assumptions. In this paper, we further decrease the Barraco-Hamity’s bound to $B \simeq 0.3636403$ $(< 3/8)$ by adding the subluminal (slower-than-light) condition of sound speed. In our analysis, we solve numerically Tolman-Oppenheimer-Volkoff equations, and the mass-to-radius ratio is maximized by variation of mass, radius and pressure inside the fluid ball as functions of mass density.

### Maximum mass of a barotropic spherical star

The ratio of total mass $M$ to surface radius $R$ of spherical perfect fluid ball has an upper bound, $M/R < B$. Buchdahl obtained $B = 4/9$ under the assumptions; non-increasing mass density in outward direction, and barotropic equation of states. Barraco and Hamity decreased the Buchdahl’s bound to a lower value $B = 3/8$ $(< 4/9)$ by adding the dominant energy condition to Buchdahl’s assumptions. In this paper, we further decrease the Barraco-Hamity’s bound to $B \simeq 0.3636403$ $(< 3/8)$ by adding the subluminal (slower-than-light) condition of sound speed. In our analysis, we solve numerically Tolman-Oppenheimer-Volkoff equations, and the mass-to-radius ratio is maximized by variation of mass, radius and pressure inside the fluid ball as functions of mass density.

### Froissart Bound on Inelastic Cross Section Without Unknown Constants [Replacement]

Assuming that axiomatic local field theory results hold for hadron scattering, Andr\’e Martin and S. M. Roy recently obtained absolute bounds on the D-wave below threshold for pion-pion scattering and thereby determined the scale of the logarithm in the Froissart bound on total cross sections in terms of pion mass only. Previously, Martin proved a rigorous upper bound on the inelastic cross-section $\sigma_{inel}$ which is one-fourth of the corresponding upper bound on $\sigma_{tot}$, and Wu, Martin,Roy and Singh improved the bound by adding the constraint of a given $\sigma_{tot}$. Here we use unitarity and analyticity to determine, without any high energy approximation, upper bounds on energy averaged inelastic cross sections in terms of low energy data in the crossed channel. These are Froissart-type bounds without any unknown coefficient or unknown scale factors and can be tested experimentally. Alternatively, their asymptotic forms,together with the Martin-Roy absolute bounds on pion-pion D-waves below threshold, yield absolute bounds on energy-averaged inelastic cross sections. E.g. for $\pi^0 \pi^0$ scattering, defining $\sigma_{inel}=\sigma_{tot} -\big (\sigma^{\pi^0 \pi^0 \rightarrow \pi^0 \pi^0} + \sigma^{\pi^0 \pi^0 \rightarrow \pi^+ \pi^-} \big )$,we show that for c.m. energy $\sqrt{s}\rightarrow \infty$, $\bar{\sigma}_{inel }(s,\infty)\equiv s\int_{s} ^{\infty } ds’\sigma_{inel }(s’)/s’^2 \leq (\pi /4) (m_{\pi })^{-2} [\ln (s/s_1)+(1/2)\ln \ln (s/s_1) +1]^2$ where $1/s_1= 34\pi \sqrt{2\pi }\>m_{\pi }^{-2}$ . This bound is asymptotically one-fourth of the corresponding Martin-Roy bound on the total cross section, and the scale factor $s_1$ is one-fourth of the scale factor in the total cross section bound. The average over the interval (s,2s) of the inelastic $\pi^0 \pi^0$cross section has a bound of the same form with $1/s_1$ replaced by $1/s_2=2/s_1$.

### Froissart Bound on Inelastic Cross Section Without Unknown Constants

Assuming that axiomatic local field theory results hold for hadron scattering, Andr\’e Martin and S. M. Roy recently obtained absolute bounds on the D-wave below threshold for pion-pion scattering and thereby determined the scale of the logarithm in the Froissart bound on total cross sections in terms of pion mass only. Previously, Martin proved a rigorous upper bound on the inelastic cross-section $\sigma_{inel}$ which is one-fourth of the corresponding upper bound on $\sigma_{tot}$, and Wu, Martin,Roy and Singh improved the bound by adding the constraint of a given $\sigma_{tot}$. Here we use unitarity and analyticity to determine, without any high energy approximation, upper bounds on energy averaged inelastic cross sections in terms of low energy data in the crossed channel. These are Froissart-type bounds without any unknown coefficient or unknown scale factors and can be tested experimentally. Alternatively, their asymptotic forms,together with the Martin-Roy absolute bounds on pion-pion D-waves below threshold, yield absolute bounds on energy-averaged inelastic cross sections. E.g. for $\pi^0 \pi^0$ scattering, defining $\sigma_{inel}=\sigma_{tot} -\big (\sigma^{\pi^0 \pi^0 \rightarrow \pi^0 \pi^0} + \sigma^{\pi^0 \pi^0 \rightarrow \pi^+ \pi^-} \big )$,we show that for c.m. energy $\sqrt{s}\rightarrow \infty$, $\bar{\sigma}_{inel }(s,\infty)\equiv s\int_{s} ^{\infty } ds’\sigma_{inel }(s’)/s’^2 \leq (\pi /4) (m_{\pi })^{-2} [\ln (s/s_1)+(1/2)\ln \ln (s/s_1) +1]^2$ where $1/s_1= 34\pi \sqrt{2\pi }\>m_{\pi }^{-2}$ . This bound is asymptotically one-fourth of the corresponding Martin-Roy bound on the total cross section, and the scale factor $s_1$ is one-fourth of the scale factor in the total cross section bound. The average over the interval (s,2s) of the inelastic $\pi^0 \pi^0$cross section has a bound of the same form with $1/s_1$ replaced by $1/s_2=2/s_1$.

### Perturbative Unitarity Constraints on Charged/Colored Portals

Dark matter that was once in thermal equilibrium with the Standard Model is generally prohibited from obtaining all of its mass from the electroweak or QCD phase transitions. This implies a new scale of physics and mediator particles needed to facilitate dark matter annihilations. In this work, we consider scenarios where thermal dark matter annihilates via scalar mediators that are colored and/or electrically charged. We show how partial wave unitarity places upper bounds on the masses and couplings on both the dark matter and mediators. To do this, we employ effective field theories with dark matter as well as three flavors of sleptons or squarks with minimum flavor violation. For Dirac (Majorana) dark matter that annihilates via mediators charged as left-handed sleptons, we find an upper bound around 45 TeV (7 TeV) for both the mediator and dark matter masses, respectively. These bounds vary as the square root of the number of colors times the number of flavors involved. Therefore the bounds diminish by root two for right handed selectrons. The bounds increase by root three and root six for right and left handed squarks, respectively. Finally, because of the interest in natural models, we also focus on an effective field theory with only stops. We find an upper bound around 32 TeV (5 TeV) for both the Dirac (Majorana) dark matter and stop masses. In comparison to traditional naturalness arguments, the stop bound gives a firmer, alternative expectation on when new physics will appear. Similar to naturalness, all of the bounds quoted above are valid outside of a defined fine-tuned regions where the dark matter can co-annihilate. The bounds in this region of parameter space can exceed the well-known bounds from Griest and Kamionkowski. We briefly describe the impact on planned and existing direct detection experiments and colliders.

### Boundaries on Neutrino Mass from Supernovae Neutronization Burst by Liquid Argon Experiments

This work presents an upper bound on the neutrino mass using the emission of $\nu_e$ from the neutronization burst of a core collapsing supernova at 10~kpc of distance and a progenitor star of 15~M$_\odot$. The calculations were done considering a 34 kton Liquid Argon Time Projection Chamber similar to the Far Detector proposal of the Long Baseline Neutrino Experiment (LBNE). We have performed a Monte Carlo simulation for the number of events integrated in 5~ms bins. Our results are $m_\nu<2.71$~eV and $0.18~\mbox{eV}<m_\nu<1.70$~eV, at 95\% C.L, assuming normal hierarchy and inverted hierarchy, respectively. We have analysed different configurations for the detector performance resulting in neutrino mass bound of $\mathcal{O}(1)$~eV.

### Upper bounds on sparticle masses from muon g-2 and the Higgs mass and the complementarity of future colliders

Supersymmetric (SUSY) explanation of the discrepancy between the measurement of $(g-2)_\mu$ and its SM prediction puts strong upper bounds on the chargino and smuon masses. At the same time, lower experimental limits on the chargino and smuon masses, combined with the Higgs mass measurement, lead to an upper bound on the stop masses. The current LHC limits on the chargino and smuon masses (for not too compressed spectrum) set the upper bound on the stop masses of about 10 TeV. The discovery potential of the future lepton and hadron colliders should lead to the discovery of SUSY if it is responsible for the explanation of the $(g-2)_\mu$ anomaly. This conclusion follows from the fact that the upper bound on the stop masses decreases with the increase of the lower experimental limit on the chargino and smuon masses.

### Upper bounds on sparticle masses from muon g-2 and the Higgs mass and the complementarity of future colliders [Replacement]

Supersymmetric (SUSY) explanation of the discrepancy between the measurement of $(g-2)_\mu$ and its SM prediction puts strong upper bounds on the chargino and smuon masses. At the same time, lower experimental limits on the chargino and smuon masses, combined with the Higgs mass measurement, lead to an upper bound on the stop masses. The current LHC limits on the chargino and smuon masses (for not too compressed spectrum) set the upper bound on the stop masses of about 10 TeV. The discovery potential of the future lepton and hadron colliders should lead to the discovery of SUSY if it is responsible for the explanation of the $(g-2)_\mu$ anomaly. This conclusion follows from the fact that the upper bound on the stop masses decreases with the increase of the lower experimental limit on the chargino and smuon masses.

### Viscosity bound for anisotropic superfluids in higher derivative gravity [Replacement]

In the present paper, based on the principles of gauge/gravity duality we analytically compute the shear viscosity to entropy ratio corresponding to the superfluid phase in Einstein Gauss-Bonnet gravity. From our analysis we note that the ratio indeed receives a finite temperature correction below certain critical temperature. This proves the non universality of shear viscosity to entropy ratio in higher derivative theories of gravity. We also compute the upper bound for the Gauss-Bonnet coupling corresponding to the symmetry broken phase and note that the upper bound on the coupling does not seem to change as long as we are close to the critical point of the phase diagram. However the corresponding lower bound of the shear viscosity to entropy ratio seems to get modified due to the finite temperature effects.

### Viscosity bound for anisotropic superfluids in higher derivative gravity

In the present paper, based on the principles of gauge/gravity duality we analytically compute the shear viscosity to entropy ratio corresponding to the superfluid phase in Einstein Gauss-Bonnet gravity. From our analysis we note that the ratio indeed receives a finite temperature correction below certain critical temperature. This proves the non universality of shear viscosity to entropy ratio in higher derivative theories of gravity. We also compute the upper bound for the Gauss-Bonnet coupling corresponding to the symmetry broken phase and note that the upper bound on the coupling does not seem to change as long as we are close to the critical point of the phase diagram. However the corresponding lower bound of the shear viscosity to entropy ratio seems to get modified due to the finite temperature effects.

### The LHC data and an upper bound for the inelastic diffraction

We comment on the status of the Pumplin bound for the inelastic diffraction in the light of the recent LHC data for elastic scattering

### Bounds on Invisible Higgs boson Decays from $t\bar{t}H$ Production

We present an upper bound on the branching fraction of the Higgs boson to invisible particles, by recasting a CMS search for stop quarks decaying to $t\bar{t}+\missET$. The observed (expected) bound, BF($H\rightarrow$inv.$)<0. 40 (0.65)$ at 95\% CL, is the strongest direct limit to date, benefiting from a downward fluctuation in the CMS data in that channel. In addition, we combine this new constraint with existing published constraints to give an observed (expected) bound of BF($H\rightarrow$inv.$)<0. 40 (0.40)$ at 95\% CL, and show some of the implications for theories of dark matter which communicate through the Higgs portal.

### The end of the MACHO era- revisited: new limits on MACHO masses from halo wide binaries

In order to determine an upper bound for the mass of the massive compact halo objets (MACHOs) we use the halo binaries contained in a recent catalog (Allen \& Monroy-Rodr\’{\i}guez 2013). To dynamically model their interactions with massive perturbers a Monte Carlo simulation is conducted, using an impulsive approximation method and assuming a galactic halo constituted by massive particles of a characteristic mass. The results of such simulations are compared with several subsamples of our improved catalog of candidate halo wide binaries. In accordance with Quinn et al. (2009) we also find our results to be very sensitive to the widest binaries. However, our larger sample, together with the fact that we can obtain galactic orbits for 150 of our systems, allows a more reliable estimate of the maximum MACHO mass than that obtained previously. If we employ the entire sample of 211 candidate halo stars we obtain an upper limit of $112 M_\sun$. However, using the 150 binaries in our catalog with computed galactic orbits we are able to refine our fitting criteria. Thus, for the 100 most halo-like binaries we obtain a maximum MACHO mass of $21-68 M_\sun$. Furthermore, we can estimate the dynamical effects of the galactic disk using binary samples that spend progressively shorter times within the disk. By extrapolating the limits obtained for our most reliable -albeit smallest- sample we find that as the time spent within the disk tends to zero the upper bound of the MACHO mass tends to less than $5 M_\sun$. The non-uniform density of the halo has also been taken into account, but the limit obtained, less than $5 M_\sun$, does not differ much from the previous one. Together with microlensing studies that provide lower limits on the MACHO mass, our results essentially exclude the existence of such objects in the galactic halo.

### Perturbative $\lambda$-Supersymmetry and Small $\kappa$-Phenomenology [Replacement]

For the minimal $\lambda$-supersymmetry, it stays perturbative to the GUT scale for $\lambda \leq 0.7$. This upper bound is relaxed when one either takes the criteria that all couplings close to $\sim 4\pi$ for non-perturbation or allows new fields at the intermediate scale between the weak and GUT scale. We show that a hidden $U(1)_X$ gauge sector with spontaneously broken scale $\sim10$ TeV improves this bound as $\lambda\leq1.23$ instead. This may induce significant effects on Higgs physics such as decreasing fine tuning involving the Higgs scalar mass, as well as on the small $\kappa$-phenomenology.

### Perturbative $\lambda$-Supersymmetry and Small $\kappa$-Phenomenology

For the minimal $\lambda$-supersymmetry, it stays perturbative to GUT scale if $\lambda \leq 0.7$. This upper bound can be relaxed if one either takes the criteria for non-perturbation when coupling closes to $\sim 4\pi$ or allows new fields at intermediate scale. It is shown that a simple $U(1)_X$ gauge sector with spontaneously broken scale $\sim10$ TeV improves the bound as $\lambda\leq1.2$ instead. This deviation can induce significant effects on Higgs physics such as decreasing fine tuning involving Higgs mass, as well as on small $\kappa$-phenomenology, the latter of which will be revised for $\lambda$ in this new range.

### Perturbative $λ$-Supersymmetry and Small $κ$-Phenomenology [Replacement]

For the minimal $\lambda$-supersymmetry, it stays perturbative to the GUT scale for $\lambda \leq 0.7$. This upper bound is relaxed when one either takes the criteria that all couplings close to $\sim 4\pi$ for non-perturbation or allows new fields at the intermediate scale between the weak and GUT scale. We show that a hidden $U(1)_X$ gauge sector with spontaneously broken scale $\sim10$ TeV improves this bound as $\lambda\leq1.3$ instead. This may induce significant effects on Higgs physics such as decreasing fine tuning involving the Higgs scalar mass, as well as on the small $\kappa$-phenomenology.

### Perturbative $\lambda$-Supersymmetry and Small $\kappa$-Phenomenology [Replacement]

For the minimal $\lambda$-supersymmetry, it stays perturbative to GUT scale if $\lambda \leq 0.7$. This upper bound can be relaxed if one either takes the criteria for non-perturbation when coupling closes to $\sim 4\pi$ or allows new fields at intermediate scale. It is shown that a simple $U(1)_X$ gauge sector with spontaneously broken scale $\sim10$ TeV improves the bound as $\lambda\leq1.2$ instead. This deviation can induce significant effects on Higgs physics such as decreasing fine tuning involving Higgs mass, as well as on small $\kappa$-phenomenology, the latter of which will be revised for $\lambda$ in this new range.

### Upper Bound on the Tensor-to-Scalar Ratio in GUT-Scale Supersymmetric Hybrid Inflation [Replacement]

We explore the upper bound on the tensor-to-scalar ratio $r$ in supersymmetric (F-term) hybrid inflation models with the gauge symmetry breaking scale set equal to the value $2.86\cdot10^{16} {\rm GeV}$, as dictated by the unification of the MSSM gauge couplings. We employ a unique renormalizable superpotential and a quasi-canonical K\"ahler potential, and the scalar spectral index $n_s$ is required to lie within the two-sigma interval from the central value found by the Planck satellite. In a sizable region of the parameter space the potential along the inflationary trajectory is a monotonically increasing function of the inflaton, and for this case, $r\lesssim2.9\cdot10^{-4}$, while the spectral index running, $|dn_{\rm s}/d\ln k|$, can be as large as $0.01$. Ignoring higher order terms which ensure the boundedness of the potential for large values of the inflaton, the upper bound on $r$ is significantly larger, of order $0.01$, for subplanckian values of the inflaton, and $|dn_{\rm s}/d\ln k|\simeq0.006$.

### Upper Bound on the Tensor-to-Scalar Ratio in GUT-Scale Supersymmetric Hybrid Inflation [Replacement]

We explore the upper bound on the tensor-to-scalar ratio $r$ in supersymmetric (F-term) hybrid inflation models with the gauge symmetry breaking scale set equal to the value $2.86\cdot10^{16} {\rm GeV}$, as dictated by the unification of the MSSM gauge couplings. We employ a unique renormalizable superpotential and a quasi-canonical K\"ahler potential, and the scalar spectral index $n_s$ is required to lie within the two-sigma interval from the central value found by the Planck satellite. In a sizable region of the parameter space the potential along the inflationary trajectory is a monotonically increasing function of the inflaton, and for this case, $r\lesssim2.9\cdot10^{-4}$, while the spectral index running, $|dn_{\rm s}/d\ln k|$, can be as large as $0.01$. Ignoring higher order terms which ensure the boundedness of the potential for large values of the inflaton, the upper bound on $r$ is significantly larger, of order $0.01$, for subplanckian values of the inflaton, and $|dn_{\rm s}/d\ln k|\simeq0.006$.

### Upper Bound on the Tensor-to-Scalar Ratio in GUT-Scale Supersymmetric Hybrid Inflation [Cross-Listing]

We explore the upper bound on the tensor-to-scalar ratio $r$ in supersymmetric (F-term) hybrid inflation models with the gauge symmetry breaking scale set equal to the value $2.86\cdot10^{16} {\rm GeV}$, as dictated by the unification of the MSSM gauge couplings. We employ a unique renormalizable superpotential and a quasi-canonical K\"ahler potential, and the scalar spectral index $n_s$ is required to lie within the two-sigma interval from the central value found by the Planck satellite. In a sizable region of the parameter space the potential along the inflationary trajectory is a monotonically increasing function of the inflaton, and for this case, $r\lesssim2.9\cdot10^{-4}$, while the spectral index running, $|dn_{\rm s}/d\ln k|$, can be as large as $0.01$. Ignoring higher order terms which ensure the boundedness of the potential for large values of the inflaton, the upper bound on $r$ is significantly larger, of order $0.01$, for subplanckian values of the inflaton, and $|dn_{\rm s}/d\ln k|\simeq0.006$.

### Upper Bound on the Tensor-to-Scalar Ratio in GUT-Scale Supersymmetric Hybrid Inflation

We explore the upper bound on the tensor-to-scalar ratio $r$ in supersymmetric (F-term) hybrid inflation models with the gauge symmetry breaking scale set equal to the value $2.86\cdot10^{16} {\rm GeV}$, as dictated by the unification of the MSSM gauge couplings. We employ a unique renormalizable superpotential and a quasi-canonical K\"ahler potential, and the scalar spectral index $n_s$ is required to lie within the two-sigma interval from the central value found by the Planck satellite. In a sizable region of the parameter space the potential along the inflationary trajectory is a monotonically increasing function of the inflaton, and for this case, $r\lesssim2.9\cdot10^{-4}$, while the spectral index running, $|dn_{\rm s}/d\ln k|$, can be as large as $0.01$. Ignoring higher order terms which ensure the boundedness of the potential for large values of the inflaton, the upper bound on $r$ is significantly larger, of order $0.01$, for subplanckian values of the inflaton, and $|dn_{\rm s}/d\ln k|\simeq0.006$.

### Upper Bound on the First Star Formation History

Our understanding of the nature of the extragalactic background light (EBL) has improved with the recent development of gamma-ray observation techniques. An open subject in the context of the EBL is the reionization epoch, which is an important probe of the formation history of first stars, the so-called Population III (Pop III) stars. Although the mechanisms for the formation of Pop III stars are rather well understood on theoretical grounds, their formation history is still veiled in mystery because of their faintness. To shed light into this matter, we study jointly the gamma-ray opacity of distant objects and the reionization constraints from studies of intergalactic gas. By combining these studies, we obtain a sensitive upper bound on the Pop III star formation rate density as $\dot\rho_{*}(z)<0.01[(1+z)/{(1+7.0)}]^{3.4}({f_{\rm esc}}/{0.2})^{-1}({C}/{3.0})\ {\rm M}_{\odot} {\rm yr}^{-1}\ {\rm Mpc}^{-3}$ at $z\ge7$, where $f_{\rm esc}$ and $C$ are the escape fraction of ionizing photons from galaxies and the clumping factor of the intergalactic hydrogen gas. This limit is a $\sim10$ times tighter constraint compared with previous studies that take into account gamma-ray opacity constraints only. Even if we do not include the current gamma-ray constraints, the results do not change. This is because the detected gamma-ray sources are still at $z\le4.35$ where the reionization has already finished.

### Bounds on Operator Dimensions in 2D Conformal Field Theories [Replacement]

We extend the work of Hellerman (arxiv:0902.2790) to derive an upper bound on the conformal dimension $\Delta_2$ of the next-to-lowest nontrival primary operator in unitary two-dimensional conformal field theories without chiral primary operators. The bound we find is of the same form as found for $\Delta_1$: $\Delta_2 \leq c_{tot}/12 + O(1)$. We find a similar bound on the conformal dimension $\Delta_3$, and present a method for deriving bounds on $\Delta_n$ for any $n$, under slightly modified assumptions. For asymptotically large $c_{tot}$ and fixed $n$, we show that $\Delta_n \leq \frac{c_{tot}}{12}+O(1)$. We conclude with a brief discussion of the gravitational implications of these results.

### A First Experimental Limit on In-matter Torsion from Neutron Spin Rotation in Liquid He-4 [Replacement]

We report the first experimental upper bound to our knowledge on possible in-matter torsion interactions of the neutron from a recent search for parity violation in neutron spin rotation in liquid He-4. Our experiment constrains a coefficient $\zeta$ consisting of a linear combination of parameters involving the time components of the torsion fields $T^\mu$ and $A^\mu$ from the nucleons and electrons in helium which violates parity. We report an upper bound of $|\zeta|<5.4×10^{-16}$ GeV at 68% confidence level and indicate other physical processes that could be analyzed to constrain in-matter torsion.

### A First Experimental Limit on In-matter Torsion from Neutron Spin Rotation in Liquid He-4 [Replacement]

We report the first experimental upper bound to our knowledge on possible in-matter torsion interactions of the neutron from a recent search for parity violation in neutron spin rotation in liquid He-4. Our experiment constrains a coefficient $\zeta$ consisting of a linear combination of parameters involving the time components of the torsion fields $T^\mu$ and $A^\mu$ from the nucleons and electrons in helium which violates parity. We report an upper bound of $|\zeta|<5.4×10^{-16}$ GeV at 68% confidence level and indicate other physical processes that could be analyzed to constrain in-matter torsion.

### A First Experimental Limit on In-matter Torsion from Neutron Spin Rotation in Liquid He-4 [Replacement]

We report the first experimental upper bound to our knowledge on possible in-matter torsion interactions of the neutron from a recent search for parity violation in neutron spin rotation in liquid He-4. Our experiment constrains a coefficient $\zeta$ consisting of a linear combination of parameters involving the time components of the torsion fields $T^\mu$ and $A^\mu$ from the nucleons and electrons in helium which violates parity. We report an upper bound of $|\zeta|<5.4×10^{-16}$ GeV at 68% confidence level and indicate other physical processes that could be analyzed to constrain in-matter torsion.

### Constraints on the conservation-law/preferred-frame $\alpha_3$ parameter from orbital motions [Cross-Listing]

We analytically calculate some orbital effects induced by the Lorentz-invariance/momentum-conservation PPN parameter $\alpha_3$ in a gravitationally bound binary system made of a compact primary orbited by a test particle. We neither restrict ourselves to any particular orbital configuration nor to specific orientations of the primary’s spin axis. We use our results to put constraints on $|\alpha_3|$ in the weak-field regime by using the latest data from Solar System planetary dynamics. From the supplementary perihelion precessions determined with the EPM2011 ephemerides, we preliminarily infer $|\alpha_3|<= 9 x 10^{-11}$, which is about 3 orders of magnitude better than the previous weak-field constraints existing in the literature. The wide pulsar-white dwarf binary PSR J0407+1607 yields an upper bound on the strong-field version of the Lorentz-invariance/momentum-conservation PPN parameter ranging from 6 x $10^{-18}$ up to to 9 x $10^{-13}$ depending on the unknown values of the pulsar’s spin axis orientation and of the orbital node and inclination. We do not recur to statistical arguments involving more than one pulsar.

### Constraints on the conservation-law/preferred-frame $\alpha_3$ parameter from orbital motions

We analytically calculate some orbital effects induced by the Lorentz-invariance/momentum-conservation PPN parameter $\alpha_3$ in a gravitationally bound binary system made of a compact primary orbited by a test particle. We neither restrict ourselves to any particular orbital configuration nor to specific orientations of the primary’s spin axis. We use our results to put constraints on $|\alpha_3|$ in the weak-field regime by using the latest data from Solar System planetary dynamics. From the supplementary perihelion precessions determined with the EPM2011 ephemerides, we preliminarily infer $|\alpha_3|<= 9 x 10^{-11}$, which is about 3 orders of magnitude better than the previous weak-field constraints existing in the literature. The wide pulsar-white dwarf binary PSR J0407+1607 yields an upper bound on the strong-field version of the Lorentz-invariance/momentum-conservation PPN parameter ranging from 6 x $10^{-18}$ up to to 9 x $10^{-13}$ depending on the unknown values of the pulsar’s spin axis orientation and of the orbital node and inclination. We do not recur to statistical arguments involving more than one pulsar.

### Spectral Distortion in a Radially Inhomogeneous Cosmology

The spectral distortion of the cosmic microwave background blackbody spectrum in a radially inhomogeneous spacetime, designed to exactly reproduce a LambdaCDM expansion history along the past light cone, is shown to exceed the upper bound established by COBE-FIRAS by a factor of approximately 3000. This simple observational test helps uncover a slew of pathological features that lie hidden inside the past light cone, including a radially contracting phase at decoupling and, if followed to its logical extreme, a naked singularity at the radially inhomogeneous Big Bang.

### Particle Production during Inflation in Light of PLANCK

We consider trapped inflation in a higher dimensional field space: particle production at a dense distribution of extra species points leads to a terminal velocity at which inflation can be driven in steep potentials. We compute an additional, nearly scale invariant contribution to the power-spectrum, caused by back-scattering of the continuously produced particles. Since this contribution has a blue tilt, it has to be sub-dominant, leading to an upper bound on the coupling constant between the inflatons and the extra species particles. We comment on the allowed parameter space, which remains relatively broad. We further show that the currently observed red spectrum is consistent with inflation driven at the terminal velocity, while the need for functional fine tuning (the eta-problem) is reduced. A tensor to scalar ratio of r = 4 (1-n_s) is a firm prediction, which is in tension with current Planck results. An absence of gravitational waves at this level would rule out trapped inflation of this type, and limits the presence of extra species points during inflation.

### Particle Production during Inflation in Light of PLANCK [Cross-Listing]

We consider trapped inflation in a higher dimensional field space: particle production at a dense distribution of extra species points leads to a terminal velocity at which inflation can be driven in steep potentials. We compute an additional, nearly scale invariant contribution to the power-spectrum, caused by back-scattering of the continuously produced particles. Since this contribution has a blue tilt, it has to be sub-dominant, leading to an upper bound on the coupling constant between the inflatons and the extra species particles. We comment on the allowed parameter space, which remains relatively broad. We further show that the currently observed red spectrum is consistent with inflation driven at the terminal velocity, while the need for functional fine tuning (the eta-problem) is reduced. A tensor to scalar ratio of r = 4 (1-n_s) is a firm prediction, which is in tension with current Planck results. An absence of gravitational waves at this level would rule out trapped inflation of this type, and limits the presence of extra species points during inflation.

### Constraining Primordial Magnetic Fields by CMB Photon-Graviton Conversion

We revisit the method of using the photon-graviton conversion mechanism in the presence of the external magnetic field to probe small-scale primordial magnetic fields that may exist between the last scattering surface and present. Specifically, we investigate impacts on the conversion efficiency due to the presence of matter, including the plasma collective effect and the atomic polarizability. In general, these effects tend to reduce the conversion probability. Under this more realistic picture and based on the precision of COBE’s measurement of CMB (cosmic microwave background) blackbody spectrum, we find an upper bound for the primordial magnetic field strength, B < 30G, at the time of recombination. Although at present the bound based on the photon-graviton conversion mechanism is not as tight as that obtained by the direct use of CMB temperature anisotropy, it nevertheless provides an important independent constraint on primordial magnetic fields and at epochs in addition to the recombination. The bound can be significantly improved if the CMB blackbody spectrum measurement becomes more precise in future experiments such as PIXIE.

### Constraining cosmic string parameters with curl mode of CMB lensing

We present constraints on a cosmic string network with a measurement of weak gravitational lensing from CMB temperature map. The cosmic string network between observer and last scattering surface of CMB photons generates vector and/or tensor metric perturbations, and the deflection of CMB photons by these gravitational fields has curl mode which is not produced by the scalar metric perturbations. To constrain cosmic string parameters, we use the power spectrum of curl mode obtained from Planck, and also, as an independent data set, from Atacama Cosmology Telescope (ACT) 2008 season data. Based on the curl mode power spectrum, we constrain the string tension, G\mu, and the reconnection probability, P. Assuming P=1, the upper bound on tension is G\mu =6.6\times 10^{-5} with 2\sigma, using curl mode from Planck, which is weaker than that from the small-scale temperature power spectrum. For small values of P, however, the constraint from curl mode becomes tighter compared to that from temperature power spectrum. For P \lsim 10^{-2}, we obtain the constraint on the combination of the string parameters as G\mu P^{-1} \leq 3.4 \times 10^{-5} at more than 2\sigma.

### Area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory [Replacement]

We prove area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory. Our inspiration comes on the one hand from a corresponding upper bound for the area in terms of the charges obtained recently by Dain, Jaramillo and Reiris [1] in the pure Einstein-Maxwell case without symmetries, and on the other hand from Yazadjiev’s inequality [2] in the axially symmetric Einstein-Maxwell-dilaton case. The common issue in these proofs and in the present one is a functional ${\mathscr W}$ of the matter fields for which the stability condition readily yields an {\it upper} bound. On the other hand, the step which crucially depends on whether or not a dilaton field is present is to obtain a {\it lower} bound for ${\mathscr W}$ as well. We obtain the latter by first setting up a variational principle for ${\mathscr W}$ with respect to the dilaton field $\phi$, then by proving existence of a minimizer $\psi$ as solution of the corresponding Euler-Lagrange equations and finally by estimating ${\mathscr W}(\psi)$. In the special case that the normal components of the electric and magnetic fields are proportional we obtain the area bound $A \ge 8\pi P Q$ in terms of the electric and magnetic charges. In the generic case our results are less explicit but imply rigorous `perturbation’ results for the above inequality. All our inequalities are saturated for a 2-parameter family of static, extreme solutions found by Gibbons [3]. Via the Bekenstein-Hawking relation $A = 4S$ our results give positive lower bounds for the entropy $S$ which are particularly interesting in the Einstein-Maxwell-dilaton case.

### Cosmic Bandits: Exploration versus Exploitation in CMB B-Mode Experiments

A preferred method to detect the curl-component, or B-mode, signature of inflationary gravitational waves (IGWs) in the cosmic microwave background (CMB) polarization, in the absence of foregrounds and lensing, is a prolonged integration over a single patch of sky of a few square degrees. In practice, however, foregrounds abound and the sensitivity to B modes can be improved considerably by finding the region of sky cleanest of foregrounds. The best strategy to detect B modes thus involves a tradeoff between exploration (to find lower-foreground patches) and exploitation (through prolonged integration). This problem is akin to the multi-armed bandit (MAB) problem in probability theory, wherein a bandit faces a series of slot machines with unknown winning odds and must develop a strategy to maximize his/her winnings with some finite number of pulls. While the optimal MAB strategy remains to be determined, a number of algorithms have been developed in an effort to maximize the winnings. Here, we formulate the search for IGW B modes in the presence of spatially-varying foregrounds as an MAB problem and develop adaptive survey strategies to optimize the sensitivity to IGW B modes. We demonstrate, using realistic foreground models and taking lensing-induced B modes into account, that adaptive experiments can substantially improve the upper bound on the tensor-to-scalar ratio (by factors of 2-3 in single frequency experiments, and possibly even more). Similar techniques can be applied to other surveys, including 21-cm measurements of signatures of the epoch of reionization, searches for a stochastic primordial gravitational wave background, deep-field imaging by the James Webb Space Telescope or various radio interferometers, and transient follow-up searches.

### Primordial black holes in non-Gaussian regimes [Replacement]

Primordial black holes (PBHs) can form in the early Universe from the collapse of rare, large density fluctuations. They have never been observed, but this fact is enough to constrain the amplitude of fluctuations on very small scales which cannot be otherwise probed. Because PBHs form only in very rare large fluctuations, the number of PBHs formed is extremely sensitive to changes in the shape of the tail of the fluctuation distribution – which depends on the amount of non-Gaussianity present. We first study how local non-Gaussianity of arbitrary size up to fifth order affects the abundance and constraints from PBHs, finding that they depend strongly on even small amounts of non-Gaussianity and the upper bound on the allowed amplitude of the power spectrum can vary by several orders of magnitude. The sign of the non-linearity parameters (f_{NL}, g_{NL}, etc) are particularly important. We also study the abundance and constraints from PBHs in the curvaton scenario, in which case the complete non-linear probability distribution is known, and find that truncating to any given order (i.e. to order f_{NL} or g_{NL}, etc) does not give accurate results.

### Primordial black holes in non-Gaussian regimes

Primordial black holes (PBHs) can form in the early Universe from the collapse of rare, large density fluctuations. They have never been observed, but this fact is enough to constrain the amplitude of fluctuations on very small scales which cannot be otherwise probed. Because PBHs form only in very rare large fluctuations, the number of PBHs formed is extremely sensitive to changes in the shape of the tail of the fluctuation distribution – which depends on the amount of non-Gaussianity present. We first study how local non-Gaussianity of arbitrary size up to fifth order affects the abundance and constraints from PBHs, finding that they depend strongly on even small amounts of non-Gaussianity and the upper bound on the allowed amplitude of the power spectrum can vary by several orders of magnitude. The sign of the non-linearity parameters (f_{NL}, g_{NL}, etc) are particularly important. We also study the abundance and constraints from PBHs in the curvaton scenario, in which case the complete non-linear probability distribution is known, and find that truncating to any given order (i.e. to order f_{NL} or g_{NL}, etc) does not give accurate results.

### The Effective Field Theory of Inflation Models with Sharp Features

We describe models of single-field inflation with small and sharp step features in the potential (and sound speed) of the inflaton field, in the context of the Effective Field Theory of Inflation. This approach allows us to study the effects of features in the power-spectrum and in the bispectrum of curvature perturbations, from a model-independent point of view, by parametrizing the features directly with modified "slow-roll" parameters. We can obtain a self-consistent power-spectrum, together with enhanced non-Gaussianity, which grows with a quantity $\beta$ that parametrizes the sharpness of the step. With this treatment it is straightforward to generalize and include features in other coefficients of the effective action of the inflaton field fluctuations. Our conclusion in this case is that, excluding extrinsic curvature terms, the only interesting effects at the level of the bispectrum could arise from features in the first slow-roll parameter $\epsilon$ or in the speed of sound $c_s$. Finally, we derive an upper bound on the parameter $\beta$ from the consistency of the perturbative expansion of the action for inflaton perturbations. This constraint can be used for an estimation of the signal-to-noise ratio, to show that the observable which is most sensitive to features is the power-spectrum. This conclusion would change if we consider the contemporary presence of a feature and a speed of sound $c_s < 1$, as, in such a case, contributions from an oscillating folded configuration can potentially make the bispectrum the leading observable for feature models.

### The Parkes Pulsar Timing Array

The aims of the Parkes Pulsar Timing Array (PPTA) project are to 1) make a direct detection of gravitational waves, 2) improve the solar system planetary ephemeris and 3) develop a pulsar-based time scale. In this article we describe the project, explain how the data are collected and processed and describe current research. Our current data sets are able to place an upper bound on the gravitational wave background that is the most stringent to date.

### Novel considerations about the error budget of the LAGEOS-based tests of frame-dragging with GRACE geopotential models [Cross-Listing]

A realistic assessment of the uncertainties in the even zonals of a given geopotential model must be made by directly comparing its coefficients with those of a wholly independent solution of superior formal accuracy. Otherwise, a favorable selective bias is introduced in the evaluation of the total error budget of the LAGEOS-based Lense-Thirring tests yielding likely too optimistic figures for it. By applying a novel approach which recently appeared in the literature, the second (L = 4) and the third (L = 6) even zonals turn out to be uncertain at a 2-3 10^-11 (L = 4) and 3-4 10^-11 (L = 6) level, respectively, yielding a total gravitational error of about 27-28%, with an upper bound of 37-39%. The results by Ries et al. themselves yield an upper bound for it of about 33%. The low-degree even zonals are not exclusively determined from the GRACE Satellite-to-Satellite Tracking (SST) range since they affect it with long-period, secular-like signatures over orbital arcs longer than one orbital period: GRACE SST is not accurately sensitive to such signals. Conversely, general relativity affects it with short-period effects as well. Thus, the issue of the a priori "imprinting" of general relativity itself in the GRACE-based models used so far remains open.

### Reconciliation of High Energy Scale Models of Inflation with Planck [Cross-Listing]

The inflationary cosmology paradigm is very successful in explaining the CMB anisotropy to the percent level. Besides the dependence on the inflationary model, the power spectra, spectral tilt and non-Gaussianity of the CMB temperature fluctuations also depend on the initial state of inflation. Here, we examine to what extent these observables are affected by our ignorance in the initial condition for inflationary perturbations, due to unknown new physics at a high scale $M$. For initial states that satisfy constraints from backreaction, we find that the amplitude of the power spectra could still be significantly altered, while the modification in bispectrum remains small. For such initial states, $M$ has an upper bound of a few tens of $H$, with $H$ being the Hubble parameter during inflation. We show that for $M\sim 20 H$, such initial states always (substantially) suppress the tensor to scalar ratio. In particular we show that a general choice of initial conditions can satisfactorily reconcile the simple $\frac{1}{2}m^2 \phi^2$ chaotic model with the Planck data.

### Reconciliation of High Energy Scale Models of Inflation with Planck [Replacement]

The inflationary cosmology paradigm is very successful in explaining the CMB anisotropy to the percent level. Besides the dependence on the inflationary model, the power spectra, spectral tilt and non-Gaussianity of the CMB temperature fluctuations also depend on the initial state of inflation. Here, we examine to what extent these observables are affected by our ignorance in the initial condition for inflationary perturbations, due to unknown new physics at a high scale $M$. For initial states that satisfy constraints from backreaction, we find that the amplitude of the power spectra could still be significantly altered, while the modification in bispectrum remains small. For such initial states, $M$ has an upper bound of a few tens of $H$, with $H$ being the Hubble parameter during inflation. We show that for $M\sim 20 H$, such initial states always (substantially) suppress the tensor to scalar ratio. In particular we show that a general choice of initial conditions can satisfactorily reconcile the simple ${1}{2}m^2 \phi^2$ chaotic model with the Planck data.