# Posts Tagged initial condition

## Recent Postings from initial condition

### Kerr/Fluid Duality and Caustics of Null Geodesics on a Horizon

An equation for a viscous incompressible fluid on a spheroidal surface which is dual to the perturbation around the near-near horizon extreme Kerr (n-NHEK) black hole is derived. It is also shown that an expansion scalar $\theta$ of a congruence of null geodesics on the null horizon of the perturbed n-NHEK spacetime, which is dual to a viscous incompressible fluid, is not positive semi-definite, even if initial conditions on the velocity are smooth. Unless initial conditions are elaborated, caustics of null congruence will occur on the horizon in the future. A similar result is obtained for a perturbed Schwarzschild black hole spacetime which is dual to a viscous incompressible fluid on $S^2$. An initial condition that $\theta$ be positive semi-definite at any point on $S^2$ is a necessary condition for the existence of smooth solutions to incompressible Navier-Stokes equation on $S^2$.

### Dynamical fine-tuning of initial conditions for small field inflations

Small-field inflation (SFI) is widely considered to be unnatural because an extreme fine-tuning of the initial condition is necessary for sufficiently large e-folding. In this paper, we show that the unnaturally-looking initial condition can be dynamically realised without any fine-tuning if the SFI occurs after rapid oscillations of the inflaton field and particle creations by preheating. In fact, if the inflaton field $\phi$ is coupled to another scalar field $\chi$ through the interaction $g^2 \chi^2 \phi^2$ and the vacuum energy during the small field inflation is given by $\lambda M^4$, the initial value can be dynamically set at $(\sqrt{\lambda}/g) M^2/M_{\rm pl}$, which is much smaller than the typical scale of the potential $M.$ This solves the initial condition problem in the new inflation model or some classes of the hilltop inflation models.

### Dynamical fine-tuning of initial conditions for small field inflations [Cross-Listing]

Small-field inflation (SFI) is widely considered to be unnatural because an extreme fine-tuning of the initial condition is necessary for sufficiently large e-folding. In this paper, we show that the unnaturally-looking initial condition can be dynamically realised without any fine-tuning if the SFI occurs after rapid oscillations of the inflaton field and particle creations by preheating. In fact, if the inflaton field $\phi$ is coupled to another scalar field $\chi$ through the interaction $g^2 \chi^2 \phi^2$ and the vacuum energy during the small field inflation is given by $\lambda M^4$, the initial value can be dynamically set at $(\sqrt{\lambda}/g) M^2/M_{\rm pl}$, which is much smaller than the typical scale of the potential $M.$ This solves the initial condition problem in the new inflation model or some classes of the hilltop inflation models.

### Dynamical fine-tuning of initial conditions for small field inflations [Cross-Listing]

Small-field inflation (SFI) is widely considered to be unnatural because an extreme fine-tuning of the initial condition is necessary for sufficiently large e-folding. In this paper, we show that the unnaturally-looking initial condition can be dynamically realised without any fine-tuning if the SFI occurs after rapid oscillations of the inflaton field and particle creations by preheating. In fact, if the inflaton field $\phi$ is coupled to another scalar field $\chi$ through the interaction $g^2 \chi^2 \phi^2$ and the vacuum energy during the small field inflation is given by $\lambda M^4$, the initial value can be dynamically set at $(\sqrt{\lambda}/g) M^2/M_{\rm pl}$, which is much smaller than the typical scale of the potential $M.$ This solves the initial condition problem in the new inflation model or some classes of the hilltop inflation models.

### Probing Pb+Pb collisions at $\sqrt{S_{NN}}=2760$ GeV with spectators [Cross-Listing]

There is event by event geometric as well as quantum fluctuations in the initial condition of heavy-ion collisions. The standard technique of analysing heavy-ion collisions in bins of centrality obtained from final state multiplicity averages out the various initial configurations and thus restricts the study to only a limited range of initial conditions. In this paper, we propose an additional binning in terms of total spectator neutrons in an event. This offers us a key control parameter to probe events with broader range of initial conditions providing us an opportunity to peep into events with rarer initial conditions which otherwise get masked when analysed by centrality binning alone. We find that the inclusion of spectator binning allows one to vary $\varepsilon_2$ and $\varepsilon_3$ independently. We observe that the standard scaling relation between $\displaystyle{v_2/\varepsilon_2}$ and $\frac{1}{S}\frac{dN_{\text{ch}}}{d\eta}$ exhibited by centrality bins is broken by the spectator neutron bins. However, the acoustic scaling relation between $\displaystyle{\ln\left( v_n/\varepsilon_n\right)}$ and transverse system size holds for both centrality as well as spectator bins for central to mid-central collisions. The introduction of the spectator binning allows us to tune over a wide range viscosity driven effects for events with varying initial states but similar final state multiplicity.

### Probing Pb+Pb collisions at $\sqrt{S_{NN}}=2760$ GeV with spectators [Cross-Listing]

There is event by event geometric as well as quantum fluctuations in the initial condition of heavy-ion collisions. The standard technique of analysing heavy-ion collisions in bins of centrality obtained from final state multiplicity averages out the various initial configurations and thus restricts the study to only a limited range of initial conditions. In this paper, we propose an additional binning in terms of total spectator neutrons in an event. This offers us a key control parameter to probe events with broader range of initial conditions providing us an opportunity to peep into events with rarer initial conditions which otherwise get masked when analysed by centrality binning alone. We find that the inclusion of spectator binning allows one to vary $\varepsilon_2$ and $\varepsilon_3$ independently. We observe that the standard scaling relation between $\displaystyle{v_2/\varepsilon_2}$ and $\frac{1}{S}\frac{dN_{\text{ch}}}{d\eta}$ exhibited by centrality bins is broken by the spectator neutron bins. However, the acoustic scaling relation between $\displaystyle{\ln\left( v_n/\varepsilon_n\right)}$ and transverse system size holds for both centrality as well as spectator bins for central to mid-central collisions. The introduction of the spectator binning allows us to tune over a wide range viscosity driven effects for events with varying initial states but similar final state multiplicity.

### Entropy and the Typicality of Universes

The universal validity of the second law of thermodynamics is widely attributed to a finely tuned initial condition of the universe. This creates a problem: why is the universe atypical? We suggest that the problem is an artefact created by inappropriate transfer of the traditional concept of entropy to the whole universe. Use of what we call the relational $N$-body problem as a model indicates the need to employ two distinct entropy-type concepts to describe the universe. One, which we call entaxy, is novel. It is scale-invariant and decreases as the observable universe evolves. The other is the algebraic sum of the dimensionful entropies of branch systems (isolated subsystems of the universe). This conventional additive entropy increases. In our model, the decrease of entaxy is fundamental and makes possible the emergence of branch systems and their increasing entropy. We have previously shown that all solutions of our model divide into two halves at a unique Janus point' of maximum disorder. This constitutes a common past for two futures each with its own gravitational arrow of time. We now show that these arrows are expressed through the formation of branch systems within which conventional entropy increases. On either side of the Janus point, this increase is in the same direction in every branch system. We also show that it is only possible to specify unbiased solution-determining data at the Janus point. Special properties of these mid-point data' make it possible to develop a rational theory of the typicality of universes whose governing law, as in our model, dictates the presence of a Janus point in every solution. If our self-gravitating universe is governed by such a law, then the second law of thermodynamics is a necessary direct consequence of it and does not need any special initial condition.

### Entropy and the Typicality of Universes [Replacement]

The universal validity of the second law of thermodynamics is widely attributed to a finely tuned initial condition of the universe. This creates a problem: why is the universe atypical? We suggest that the problem is an artefact created by inappropriate transfer of the traditional concept of entropy to the whole universe. Use of what we call the relational $N$-body problem as a model indicates the need to employ two distinct entropy-type concepts to describe the universe. One, which we call entaxy, is novel. It is scale-invariant and decreases as the observable universe evolves. The other is the algebraic sum of the dimensionful entropies of branch systems (isolated subsystems of the universe). This conventional additive entropy increases. In our model, the decrease of entaxy is fundamental and makes possible the emergence of branch systems and their increasing entropy. We have previously shown that all solutions of our model divide into two halves at a unique Janus point' of maximum disorder. This constitutes a common past for two futures each with its own gravitational arrow of time. We now show that these arrows are expressed through the formation of branch systems within which conventional entropy increases. On either side of the Janus point, this increase is in the same direction in every branch system. We also show that it is only possible to specify unbiased solution-determining data at the Janus point. Special properties of these mid-point data' make it possible to develop a rational theory of the typicality of universes whose governing law, as in our model, dictates the presence of a Janus point in every solution. If our self-gravitating universe is governed by such a law, then the second law of thermodynamics is a necessary direct consequence of it and does not need any special initial condition.

### Towards the physical vacuum of cosmic inflation

There have been long debates about the initial condition of inflationary perturbations. In this work we explicitly show the decay of excited states during inflation via interactions. For this purpose, we note that the folded shape non-Gaussianity can be interpreted as the decay of the non-Bunch-Davies initial condition. The one loop diagrams with non-Bunch-Davies propagators are calculated to uncover the decay of such excited states. The observed smallness of non-Gaussianity keeps the window open for probing inflationary initial conditions and trans-Planckian physics.

### Finite-Time Singularities in $k=0$ FLRW Cosmologies [Cross-Listing]

In this paper, we consider a spatially flat FLRW cosmological model with matter obeying a barotropic equation of state $p = w \mu$, $-1<w\leq1$, and a cosmological constant, $\Lambda$. We use Osgood's criterion to establish three cases when such models admit finite-time singularities. The first case is for an arbitrary initial condition, with a negative cosmological constant, and phantom energy $w < -1$. We show that except for a very fine-tuned choice of the initial condition $\theta_{0}$, the universe will develop a finite-time singularity. The second case we consider is for a nonnegative cosmological constant, phantom energy, and the expansion scalar being larger than that of the flat-space de Sitter solution, and show that such models only expand forever for $\Lambda = 0$. In all other cases, the universe model develops a finite-time singularity. The final case we consider is for a nonnegative cosmological constant, a matter source with $-1 < w \leq 1$, and an expansion scalar that is asymptotically that of the de Sitter universe. We show that such models will only expand forever when $\Lambda = 0$, otherwise, they will develop a finite-time singularity. This is significant, since the inflationary epoch is a subset of this domain. However, as we show, the inclusion of a bulk viscosity term in the Einstein field equations eliminates this singularity, and the universe expands forever. This could have interesting implications for the role of bulk viscosity in dynamical models of the universe.

### Finite-Time Singularities in $k=0$ FLRW Cosmologies

In this paper, we consider a spatially flat FLRW cosmological model with matter obeying a barotropic equation of state $p = w \mu$, $-1<w\leq1$, and a cosmological constant, $\Lambda$. We use Osgood's criterion to establish three cases when such models admit finite-time singularities. The first case is for an arbitrary initial condition, with a negative cosmological constant, and phantom energy $w < -1$. We show that except for a very fine-tuned choice of the initial condition $\theta_{0}$, the universe will develop a finite-time singularity. The second case we consider is for a nonnegative cosmological constant, phantom energy, and the expansion scalar being larger than that of the flat-space de Sitter solution, and show that such models only expand forever for $\Lambda = 0$. In all other cases, the universe model develops a finite-time singularity. The final case we consider is for a nonnegative cosmological constant, a matter source with $-1 < w \leq 1$, and an expansion scalar that is asymptotically that of the de Sitter universe. We show that such models will only expand forever when $\Lambda = 0$, otherwise, they will develop a finite-time singularity. This is significant, since the inflationary epoch is a subset of this domain. However, as we show, the inclusion of a bulk viscosity term in the Einstein field equations eliminates this singularity, and the universe expands forever. This could have interesting implications for the role of bulk viscosity in dynamical models of the universe.

### Finite-Time Singularities in $k=0$ FLRW Cosmologies [Replacement]

In this paper, we consider a spatially flat FLRW cosmological model with matter obeying a barotropic equation of state $p = w \mu$, $-1<w\leq1$, and a cosmological constant, $\Lambda$. We use Osgood's criterion to establish three cases when such models admit finite-time singularities. The first case is for an arbitrary initial condition, with a negative cosmological constant, and phantom energy $w < -1$. We show that except for a very fine-tuned choice of the initial condition $\theta_{0}$, the universe will develop a finite-time singularity. The second case we consider is for a nonnegative cosmological constant, phantom energy, and the expansion scalar being larger than that of the flat-space de Sitter solution, and show that such models only expand forever for $\Lambda = 0$. In all other cases, the universe model develops a finite-time singularity. The final case we consider is for a nonnegative cosmological constant, a matter source with $-1 < w \leq 1$, and an expansion scalar that is asymptotically that of the de Sitter universe. We show that such models will only expand forever when $\Lambda = 0$, otherwise, they will develop a finite-time singularity. This is significant, since the inflationary epoch is a subset of this domain. However, as we show, the inclusion of a bulk viscosity term in the Einstein field equations eliminates this singularity, and the universe expands forever. This could have interesting implications for the role of bulk viscosity in dynamical models of the universe.

### Finite-Time Singularities in $k=0$ FLRW Cosmologies [Replacement]

In this paper, we consider a spatially flat FLRW cosmological model with matter obeying a barotropic equation of state $p = w \mu$, $-1<w\leq1$, and a cosmological constant, $\Lambda$. We use Osgood's criterion to establish three cases when such models admit finite-time singularities. The first case is for an arbitrary initial condition, with a negative cosmological constant, and phantom energy $w < -1$. We show that except for a very fine-tuned choice of the initial condition $\theta_{0}$, the universe will develop a finite-time singularity. The second case we consider is for a nonnegative cosmological constant, phantom energy, and the expansion scalar being larger than that of the flat-space de Sitter solution, and show that such models only expand forever for $\Lambda = 0$. In all other cases, the universe model develops a finite-time singularity. The final case we consider is for a nonnegative cosmological constant, a matter source with $-1 < w \leq 1$, and an expansion scalar that is asymptotically that of the de Sitter universe. We show that such models will only expand forever when $\Lambda = 0$, otherwise, they will develop a finite-time singularity. This is significant, since the inflationary epoch is a subset of this domain. However, as we show, the inclusion of a bulk viscosity term in the Einstein field equations eliminates this singularity, and the universe expands forever. This could have interesting implications for the role of bulk viscosity in dynamical models of the universe.

### Standard 1D solar atmosphere as initial condition for MHD simulations and switch-on effects

Many applications in Solar physics need a 1D atmospheric model as initial condition or as reference for inversions of observational data. The VAL atmospheric models are based on observations and are widely used since decades. Complementary to that, the FAL models implement radiative hydrodynamics and showed the shortcomings of the VAL models since almost equally long time. In this work, we present a new 1D layered atmosphere that spans not only from the photosphere to the transition region, but from the solar interior up to far in the corona. We also discuss typical mistakes that are done when switching on simulations based on such an initial condition and show how the initial condition can be equilibrated so that a simulation can start smoothly. The 1D atmosphere we present here served well as initial condition for HD and MHD simulations and should also be considered as reference data for solving inverse problems.

### Nonassociative Weyl star products [Replacement]

Deformation quantization is a formal deformation of the algebra of smooth functions on some manifold. In the classical setting, the Poisson bracket serves as an initial conditions, while the associativity allows to proceed to higher orders. Some applications to string theory require deformation in the direction of a quasi-Poisson bracket (that does not satisfy the Jacobi identity). This initial condition is incompatible with associativity, it is quite unclear which restrictions can be imposed on the deformation. We show that for any quasi-Poisson bracket the deformation quantization exists and is essentially unique if one requires (weak) hermiticity and the Weyl condition. We also propose an iterative procedure that allows to compute the star product up to any desired order.

### What initial condition of inflation would suppress the large-scale CMB spectrum? [Cross-Listing]

There is an apparent power deficit relative to the $\Lambda$CDM prediction of the CMB spectrum at large scales, which, though not yet statistically significant, persists from WMAP to Planck data. Proposals that invoke some form of initial condition for the inflation have been made to address this apparent power suppression, albeit with conflicting conclusions. By studying the curvature perturbation spectrum of a scalar field in the FLRW Universe, we show that if the Universe begins in the era with positive or phantom pressure, the large-scale spectrum is suppressed, provided the Universe approaches to the adiabatic vacuum at small scales. It is noted that the large-scale spectrum could not be generated by causal mechanisms in the decelerating Universe since the super-horizon scales are initially across causally disconnected regions. On the other hand, as long as the Universe begins in the negative-pressure era, even if there is an intermediate era with positive-pressure, the large-scale spectrum would be enhanced rather than suppressed. The spectrum of the two-stage inflation model with a given two-field potential is further calculated, showing agreement with the conclusions obtained from the ad hoc single-field analysis.

### What initial condition of inflation would suppress the large-scale CMB spectrum?

There is an apparent power deficit relative to the $\Lambda$CDM prediction of the CMB spectrum at large scales, which, though not yet statistically significant, persists from WMAP to Planck data. Proposals that invoke some form of initial condition for the inflation have been made to address this apparent power suppression, albeit with conflicting conclusions. By studying the curvature perturbation spectrum of a scalar field in the FLRW Universe, we show that if the Universe begins in the era with positive or phantom pressure, the large-scale spectrum is suppressed, provided the Universe approaches to the adiabatic vacuum at small scales. It is noted that the large-scale spectrum could not be generated by causal mechanisms in the decelerating Universe since the super-horizon scales are initially across causally disconnected regions. On the other hand, as long as the Universe begins in the negative-pressure era, even if there is an intermediate era with positive-pressure, the large-scale spectrum would be enhanced rather than suppressed. The spectrum of the two-stage inflation model with a given two-field potential is further calculated, showing agreement with the conclusions obtained from the ad hoc single-field analysis.

### What initial condition of inflation would suppress the large-scale CMB spectrum? [Replacement]

There is an apparent power deficit relative to the $\Lambda$CDM prediction of the CMB spectrum at large scales, which, though not yet statistically significant, persists from WMAP to Planck data. Proposals that invoke some form of initial condition for the inflation have been made to address this apparent power suppression, albeit with conflicting conclusions. By studying the curvature perturbations of a scalar field in the FLRW universe, we find that the large-scale spectrum at the end of inflation reflects the super-horizon spectrum of the initial state. The large-scale spectrum is suppressed if the universe begins with the adiabatic vacuum in a super-inflation or positive-pressure era. In the latter case, there is however no causal mechanism to establish the initial adiabatic vacuum. On the other hand, as long as the universe begins with the adiabatic vacuum in a negative-pressure era, even if there exists an intermediate positive-pressure era, the large-scale spectrum would be enhanced rather than suppressed. We further calculate the spectrum of a two-stage inflation model with a two-field potential and show that the result agrees with that obtained from the \emph{ad hoc} single-field analysis.

### Transients in finite inflation

We test a model of inflation with a fast-rolling kinetic dominated initial condition against data from Planck using MCMC. We choose a m^2 {\phi}^2 potential and perform a full numerical calculation of both the scalar and tensor primordial power spectra. We find a slight improvement in fit for this model over the standard eternal slow roll case.

### Transients in finite inflation [Cross-Listing]

We test a model of inflation with a fast-rolling kinetic dominated initial condition against data from Planck using MCMC. We choose a m^2 {\phi}^2 potential and perform a full numerical calculation of both the scalar and tensor primordial power spectra. We find a slight improvement in fit for this model over the standard eternal slow roll case.

### Transients in finite inflation [Cross-Listing]

We test a model of inflation with a fast-rolling kinetic dominated initial condition against data from Planck using MCMC. We choose a m^2 {\phi}^2 potential and perform a full numerical calculation of both the scalar and tensor primordial power spectra. We find a slight improvement in fit for this model over the standard eternal slow roll case.

### Quarks Production in the Quark-Gluon Plasma Created in Relativistic Heavy Ion Collisions [Cross-Listing]

In this article we report on our results about quark production and chemical equilibration of quark-gluon plasma. Our initial condition corresponds to a classic Yang-Mills spectrum, in which only gluon degrees of freedom are considered; the initial condition is then evolved to a quark-gluon plasma by means of relativistic transport theory with inelastic processes which permit the conversion of gluons to $q\bar{q}$ pairs. We then compare our results to the ones obtained with a standard Glauber model initialization. We find that regardless of the initial condition the final stage of the system contains an abundant percentage of $q\bar{q}$ pairs; moreover spanning the possible coupling from weak to strong we find that unless the coupling is unrealistically small, both production rate and final percentage of fermions is quite large.

### Quarks Production in the Quark-Gluon Plasma Created in Relativistic Heavy Ion Collisions [Replacement]

In this article we report on our results about quark production and chemical equilibration of quark-gluon plasma. Our initial condition corresponds to a classic Yang-Mills spectrum, in which only gluon degrees of freedom are considered; the initial condition is then evolved to a quark-gluon plasma by means of relativistic transport theory with inelastic processes which permit the conversion of gluons to $q\bar{q}$ pairs. We then compare our results to the ones obtained with a standard Glauber model initialization. We find that regardless of the initial condition the final stage of the system contains an abundant percentage of $q\bar{q}$ pairs; moreover spanning the possible coupling from weak to strong we find that unless the coupling is unrealistically small, both production rate and final percentage of fermions is quite large.

### Painleve Transcendents and PT-Symmetric Hamiltonians [Cross-Listing]

Unstable separatrix solutions for the first and second Painlev\'e transcendents are studied both numerically and analytically. For a fixed initial condition, say $y(0)=0$, there is a discrete set of initial slopes $y'(0)=b_n$ that give rise to separatrix solutions. Similarly, for a fixed initial slope, say $y'(0)= 0$, there is a discrete set of initial values $y(0)=c_n$ that give rise to separatrix solutions. For Painlev\'e I the large-$n$ asymptotic behavior of $b_n$ is $b_n\sim B_{\rm I}n^{3/5}$ and that of $c_n$ is $c_n\sim C_{\rm I}n^{2/ 5}$, and for Painlev\'e II the large-$n$ asymptotic behavior of $b_n$ is $b_n \sim B_{\rm II}n^{2/3}$ and that of $c_n$ is $c_n\sim C_{\rm II}n^{1/3}$. The constants $B_{\rm I}$, $C_{\rm I}$, $B_{\rm II}$, and $C_{\rm II}$ are first determined numerically. Then, they are found analytically and in closed form by reducing the nonlinear equations to the linear eigenvalue problems associated with the cubic and quartic PT-symmetric Hamiltonians $H=\frac{1}{2}p^2+2ix^3$ and $H=\frac{1}{2}p^2-\frac{1}{2}x^4$.

### Black hole spectra in holography: consequences for equilibration of dual gauge theories [Replacement]

For a closed system to equilibrate from a given initial condition there must exist an equilibrium state with the energy equal to the initial one. Equilibrium states of a strongly coupled gauge theory with a gravitational holographic dual are represented by black holes. We study the spectrum of black holes in Pilch-Warner geometry. These black holes are holographically dual to equilibrium states of strongly coupled $SU(N)$ ${\cal N}=2^*$ gauge theory plasma on $S^3$ in the planar limit. We find that there is no energy gap in the black hole spectrum. Thus, there is a priory no obstruction for equilibration of arbitrary low-energy states in the theory via a small black hole gravitational collapse. The latter is contrasted with phenomenological examples of holography with dual four-dimensional CFTs having non-equal central charges in the stress-energy tensor trace anomaly.

### An effective model for entropy deposition in high-energy pp, pA, and AA collisions [Cross-Listing]

We introduce TRENTO, a new initial condition model for high-energy nuclear collisions based on eikonal entropy deposition via a "reduced thickness" function. The model simultaneously predicts the shapes of experimental proton-proton, proton-nucleus, and nucleus-nucleus multiplicity distributions, and generates nucleus-nucleus eccentricity harmonics consistent with experimental flow constraints. In addition, the model provides a possible resolution to the "knee" puzzle in ultra-central uranium-uranium collisions.

### An effective model for entropy deposition in high-energy pp, pA, and AA collisions [Cross-Listing]

We introduce TRENTO, a new initial condition model for high-energy nuclear collisions based on eikonal entropy deposition via a "reduced thickness" function. The model simultaneously predicts the shapes of experimental proton-proton, proton-nucleus, and nucleus-nucleus multiplicity distributions, and generates nucleus-nucleus eccentricity harmonics consistent with experimental flow constraints. In addition, the model provides a possible resolution to the "knee" puzzle in ultra-central uranium-uranium collisions.

### Initial Condition of Relic Gravitational Waves Constrained by LIGO S6 and Multiple Interferometers

The relic gravitational wave (RGW) generated during the inflation depends on the initial condition via the amplitude, the spectral index $n_t$ and the running index $\alpha_t$. CMB observations so far have only constrained the tensor-scalar ratio $r$, but not $n_t$ nor $\alpha_t$. Complementary to this, the ground-based interferometric detectors working at $\sim 10^2$Hz are able to constrain the spectral indices that influence the spectrum sensitively at high frequencies. In this work we give a proper normalization of the analytical spectrum at the low frequency end, yielding a modification by a factor of $\sim 1/50$ to the previous treatment. We calculate the signal-noise ratios (SNR) for various ($n_t,\alpha_t$) at fixed $r=0.2$ by S6 of LIGO H-L, and obtain the observational upper limit on the running index $\alpha_t<0.02093$ (i.e, at a detection rate $95\%$ and a false alarm rate $5\%$) at the default $(n_t=0,r=0.2)$. This is consistent with the constraint on the energy density obtained by LIGO-Virgo Collaboration. Extending to the four correlated detectors currently running, the calculated SNR improves slightly. When extending to the six correlated detectors of the second-generation in design, the calculated SNR is $\sim 10^3$ times over the previous two cases, due to the high sensitivities. RGW can be directly detected by the six 2nd-generation detectors for models with $\alpha_t>0.01364$.

### Initial Condition of Relic Gravitational Waves Constrained by LIGO S6 and Multiple Interferometers [Replacement]

The relic gravitational wave (RGW) generated during the inflation depends on the initial condition via the amplitude, the spectral index $n_t$ and the running index $\alpha_t$. CMB observations so far have only constrained the tensor-scalar ratio $r$, but not $n_t$ nor $\alpha_t$. Complementary to this, the ground-based interferometric detectors working at $\sim 10^2$Hz are able to constrain the spectral indices that influence the spectrum sensitively at high frequencies. In this work we give a proper normalization of the analytical spectrum at the low frequency end, yielding a modification by a factor of $\sim 1/50$ to the previous treatment. We calculate the signal-noise ratios (SNR) for various ($n_t,\alpha_t$) at fixed $r=0.2$ by S6 of LIGO H-L, and obtain the observational upper limit on the running index $\alpha_t<0.02093$ (i.e, at a detection rate $95\%$ and a false alarm rate $5\%$) at the default $(n_t=0,r=0.2)$. This is consistent with the constraint on the energy density obtained by LIGO-Virgo Collaboration. Extending to the four correlated detectors currently running, the calculated SNR improves slightly. When extending to the six correlated detectors of the second-generation in design, the calculated SNR is $\sim 10^3$ times over the previous two cases, due to the high sensitivities. RGW can be directly detected by the six 2nd-generation detectors for models with $\alpha_t>0.01364$.

### Initial Condition of Relic Gravitational Waves Constrained by LIGO S6 and Multiple Interferometers [Cross-Listing]

The relic gravitational wave (RGW) generated during the inflation depends on the initial condition via the amplitude, the spectral index $n_t$ and the running index $\alpha_t$. CMB observations so far have only constrained the tensor-scalar ratio $r$, but not $n_t$ nor $\alpha_t$. Complementary to this, the ground-based interferometric detectors working at $\sim 10^2$Hz are able to constrain the spectral indices that influence the spectrum sensitively at high frequencies. In this work we give a proper normalization of the analytical spectrum at the low frequency end, yielding a modification by a factor of $\sim 1/50$ to the previous treatment. We calculate the signal-noise ratios (SNR) for various ($n_t,\alpha_t$) at fixed $r=0.2$ by S6 of LIGO H-L, and obtain the observational upper limit on the running index $\alpha_t<0.02093$ (i.e, at a detection rate $95\%$ and a false alarm rate $5\%$) at the default $(n_t=0,r=0.2)$. This is consistent with the constraint on the energy density obtained by LIGO-Virgo Collaboration. Extending to the four correlated detectors currently running, the calculated SNR improves slightly. When extending to the six correlated detectors of the second-generation in design, the calculated SNR is $\sim 10^3$ times over the previous two cases, due to the high sensitivities. RGW can be directly detected by the six 2nd-generation detectors for models with $\alpha_t>0.01364$.

### Initial Condition of Relic Gravitational Waves Constrained by LIGO S6 and Multiple Interferometers [Replacement]

The relic gravitational wave (RGW) generated during the inflation depends on the initial condition via the amplitude, the spectral index $n_t$ and the running index $\alpha_t$. CMB observations so far have only constrained the tensor-scalar ratio $r$, but not $n_t$ nor $\alpha_t$. Complementary to this, the ground-based interferometric detectors working at $\sim 10^2$Hz are able to constrain the spectral indices that influence the spectrum sensitively at high frequencies. In this work we give a proper normalization of the analytical spectrum at the low frequency end, yielding a modification by a factor of $\sim 1/50$ to the previous treatment. We calculate the signal-noise ratios (SNR) for various ($n_t,\alpha_t$) at fixed $r=0.2$ by S6 of LIGO H-L, and obtain the observational upper limit on the running index $\alpha_t<0.02093$ (i.e, at a detection rate $95\%$ and a false alarm rate $5\%$) at the default $(n_t=0,r=0.2)$. This is consistent with the constraint on the energy density obtained by LIGO-Virgo Collaboration. Extending to the four correlated detectors currently running, the calculated SNR improves slightly. When extending to the six correlated detectors of the second-generation in design, the calculated SNR is $\sim 10^3$ times over the previous two cases, due to the high sensitivities. RGW can be directly detected by the six 2nd-generation detectors for models with $\alpha_t>0.01364$.

### Classical and quantum effective theories

A generalization of the action principle of classical mechanics, motivated by the Closed Time Path (CTP) scheme of quantum field theory, is presented to deal with initial condition problems and dissipative forces. The similarities of the classical and the quantum cases are underlined. In particular, effective interactions which describe classical dissipative forces represent the system-environment entanglement. The relation between the traditional effective theories and their CTP extension is briefly discussed and few qualitative examples are mentioned.

### Classical and quantum effective theories [Replacement]

A generalization of the action principle of classical mechanics, motivated by the Closed Time Path (CTP) scheme of quantum field theory, is presented to deal with initial condition problems and dissipative forces. The similarities of the classical and the quantum cases are underlined. In particular, effective interactions which describe classical dissipative forces represent the system-environment entanglement. The relation between the traditional effective theories and their CTP extension is briefly discussed and few qualitative examples are mentioned.

### Effect of initial-state nucleon-nucleon correlations on collective flow in ultra-central heavy-ion collisions [Cross-Listing]

We investigate the effect of nucleon-nucleon correlations on the initial condition of ultra-central heavy ion collisions at LHC energies. We calculate the eccentricities of the MC-Glauber and IP-Glasma models in the 0--1% centrality class and show that they are considerably affected by the inclusion of such type of correlations. For an IP-Glasma initial condition, we further demonstrate that this effect survives the fluid-dynamical evolution of the system and can be observed in its final state azimuthal momentum anisotropy.

### Dipole amplitude with uncertainty estimate from HERA data and applications in Color Glass Condensate phenomenology

We determine the initial condition for the small-$x$ evolution equation (BK) from the HERA deep inelastic scattering data using a new parametrization that also keeps the unintegrated gluon distribution positive. The obtained dipole amplitude and its uncertainty estimate can be used to compute single inclusive particle production in proton-proton and proton-nucleus collisions. We argue that one has to use consistently the proton transverse area measured in DIS and the total inelastic cross section when calculating the single inclusive cross section. This leads to a midrapidity nuclear modification factor $R_{pA}$ that approaches unity at large transverse momentum, independently of the center-of-mass energy.

### Quantum cosmological consistency condition for inflation [Replacement]

We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the initial condition for inflation and therefore as a quantum cosmological prediction for its energy scale. This energy scale is also a genuine prediction of any inflationary model by itself, as the primordial gravitons generated during inflation leave their imprint in the B-polarization of the cosmic microwave background. In this way, one can derive a consistency condition for inflationary models that guarantees compatibility with a tunneling origin and can lead to a testable quantum cosmological prediction. The general method is demonstrated explicitly for the model of natural inflation.

### Quantum cosmological consistency condition for inflation [Cross-Listing]

We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the initial condition for inflation and therefore as a quantum cosmological prediction for its energy scale. This energy scale is also a genuine prediction of any inflationary model by itself, as the primordial gravitons generated during inflation leave their imprint in the B-polarization of the cosmic microwave background. In this way, one can derive a consistency condition for inflationary models that guarantees compatibility with a tunneling origin and can lead to a testable quantum cosmological prediction. The general method is demonstrated explicitly for the model of natural inflation.

### Quantum cosmological consistency condition for inflation [Replacement]

We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the initial condition for inflation and therefore as a quantum cosmological prediction for its energy scale. This energy scale is also a genuine prediction of any inflationary model by itself, as the primordial gravitons generated during inflation leave their imprint in the B-polarization of the cosmic microwave background. In this way, one can derive a consistency condition for inflationary models that guarantees compatibility with a tunneling origin and can lead to a testable quantum cosmological prediction. The general method is demonstrated explicitly for the model of natural inflation.

### Quantum cosmological consistency condition for inflation [Replacement]

We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the initial condition for inflation and therefore as a quantum cosmological prediction for its energy scale. This energy scale is also a genuine prediction of any inflationary model by itself, as the primordial gravitons generated during inflation leave their imprint in the B-polarization of the cosmic microwave background. In this way, one can derive a consistency condition for inflationary models that guarantees compatibility with a tunneling origin and can lead to a testable quantum cosmological prediction. The general method is demonstrated explicitly for the model of natural inflation.

### Quantum cosmological consistency condition for inflation [Cross-Listing]

We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the initial condition for inflation and therefore as a quantum cosmological prediction for its energy scale. This energy scale is also a genuine prediction of any inflationary model by itself, as the primordial gravitons generated during inflation leave their imprint in the B-polarization of the cosmic microwave background. In this way, one can derive a consistency condition for inflationary models that guarantees compatibility with a tunneling origin and can lead to a testable quantum cosmological prediction. The general method is demonstrated explicitly for the model of natural inflation.

### Approach to equilibrium in weakly coupled nonabelian plasmas

We follow the time evolution of nonabelian gauge bosons from far-from-equilibrium initial conditions to thermal equilibrium by numerically solving an effective kinetic equation that becomes accurate in the weak coupling limit. We consider initial conditions that are either highly overoccupied or underoccupied. We find that overoccupied systems thermalize through a turbulent cascade reaching equilibrium in multiples of a thermalization time $t\approx 72./ (1-0.12\log \lambda)/\lambda^2 T$, whereas underoccupied systems undergo a "bottom-up" thermalization in a time $t\approx (34. +21. \ln(Q/T))/ (1-0.037\log \lambda)(Q/T)^{1/2}/\lambda^2 T$, where $Q$ is the characteristic momentum scale of the initial condition. We apply this result to model initial stages of heavy-ion collisions and find rapid thermalization roughly in a time $Qt \lesssim 10$ or $t\lesssim 1$ fm/c.

### Running coupling effects in the evolution of jet quenching

We study the consequences of including the running of the QCD coupling in the equation describing the evolution of the jet quenching parameter $\hat q$ in the double logarithmic approximation. To start with, we revisit the case of a fixed coupling, for which we obtain exact solutions valid for generic values of the transverse momentum (above the medium saturation scale) and corresponding to various initial conditions. In the case of a running coupling, we construct approximate solutions in the form of truncated series obtained via successive iterations, whose convergence is well under control. We thus deduce the dominant asymptotic behavior of the renormalized $\hat q$ in the limit of a large evolution time $Y\equiv\ln(L/\lambda)$, with $L$ the size of the medium and $\lambda$ the typical wavelength of a medium constituent. We show that the asymptotic expansion is universal with respect to the choice of the initial condition at $Y=0$ and, moreover, it is remarkably similar to the corresponding expansion for the saturation momentum of a shockwave (a large nucleus). As expected, the running of the coupling significantly slows down the increase of $\hat q$ with $Y$ in the asymptotic regime at $Y\gg 1$. For the phenomenologically interesting value $Y\simeq 3$, we find an enhancement factor close to 3, independently of the initial condition and for both fixed and running coupling.

### Complexified Starobinsky Inflation in Supergravity in the Light of Recent BICEP2 Result [Cross-Listing]

Motivated by the recent observation of the $B$-mode signal in the cosmic microwave background by BICEP2, we stuty the Starobinsky-type inflation model in the framework of old-minimal supergravity, where the inflaton field in the original (non-supersymmetric) Starobinsky inflation model becomes a complex field. We study how the inflaton evolves on the two-dimensional field space, varying the initial condition. We show that (i) one of the scalar fields has a very steep potential once the trajectory is off from that of the original Starobinsky inflation, and that (ii) the $B$-mode signal observed by BICEP2 is too large to be consistent with the prediction of the model irrespective of the initial condition. Thus, the BICEP2 result strongly disfavors the complexified Starobinsky inflation in supergravity.

### Complexified Starobinsky Inflation in Supergravity in the Light of Recent BICEP2 Result [Cross-Listing]

Motivated by the recent observation of the $B$-mode signal in the cosmic microwave background by BICEP2, we stuty the Starobinsky-type inflation model in the framework of old-minimal supergravity, where the inflaton field in the original (non-supersymmetric) Starobinsky inflation model becomes a complex field. We study how the inflaton evolves on the two-dimensional field space, varying the initial condition. We show that (i) one of the scalar fields has a very steep potential once the trajectory is off from that of the original Starobinsky inflation, and that (ii) the $B$-mode signal observed by BICEP2 is too large to be consistent with the prediction of the model irrespective of the initial condition. Thus, the BICEP2 result strongly disfavors the complexified Starobinsky inflation in supergravity.

### Complexified Starobinsky Inflation in Supergravity in the Light of Recent BICEP2 Result [Replacement]

Motivated by the recent observation of the B-mode signal in the cosmic microwave background by BICEP2, we stuty the Starobinsky-type inflation model in the framework of old-minimal supergravity, where the inflaton field in the original (non-supersymmetric) Starobinsky inflation model becomes a complex field. We study how the inflaton evolves on the two-dimensional field space, varying the initial condition. We show that (i) one of the scalar fields has a very steep potential once the trajectory is off from that of the original Starobinsky inflation, and that (ii) the B-mode signal observed by BICEP2 is too large to be consistent with the prediction of the model irrespective of the initial condition. Thus, the BICEP2 result strongly disfavors the complexified Starobinsky inflation in supergravity.

### Complexified Starobinsky Inflation in Supergravity in the Light of Recent BICEP2 Result [Replacement]

Motivated by the recent observation of the B-mode signal in the cosmic microwave background by BICEP2, we stuty the Starobinsky-type inflation model in the framework of old-minimal supergravity, where the inflaton field in the original (non-supersymmetric) Starobinsky inflation model becomes a complex field. We study how the inflaton evolves on the two-dimensional field space, varying the initial condition. We show that (i) one of the scalar fields has a very steep potential once the trajectory is off from that of the original Starobinsky inflation, and that (ii) the B-mode signal observed by BICEP2 is too large to be consistent with the prediction of the model irrespective of the initial condition. Thus, the BICEP2 result strongly disfavors the complexified Starobinsky inflation in supergravity.

### Complexified Starobinsky Inflation in Supergravity in the Light of Recent BICEP2 Result [Replacement]

Motivated by the recent observation of the B-mode signal in the cosmic microwave background by BICEP2, we stuty the Starobinsky-type inflation model in the framework of old-minimal supergravity, where the inflaton field in the original (non-supersymmetric) Starobinsky inflation model becomes a complex field. We study how the inflaton evolves on the two-dimensional field space, varying the initial condition. We show that (i) one of the scalar fields has a very steep potential once the trajectory is off from that of the original Starobinsky inflation, and that (ii) the B-mode signal observed by BICEP2 is too large to be consistent with the prediction of the model irrespective of the initial condition. Thus, the BICEP2 result strongly disfavors the complexified Starobinsky inflation in supergravity.

### Complexified Starobinsky Inflation in Supergravity in the Light of Recent BICEP2 Result [Replacement]

Motivated by the recent observation of the B-mode signal in the cosmic microwave background by BICEP2, we stuty the Starobinsky-type inflation model in the framework of old-minimal supergravity, where the inflaton field in the original (non-supersymmetric) Starobinsky inflation model becomes a complex field. We study how the inflaton evolves on the two-dimensional field space, varying the initial condition. We show that (i) one of the scalar fields has a very steep potential once the trajectory is off from that of the original Starobinsky inflation, and that (ii) the B-mode signal observed by BICEP2 is too large to be consistent with the prediction of the model irrespective of the initial condition. Thus, the BICEP2 result strongly disfavors the complexified Starobinsky inflation in supergravity.

### Complexified Starobinsky Inflation in Supergravity in the Light of Recent BICEP2 Result

Motivated by the recent observation of the $B$-mode signal in the cosmic microwave background by BICEP2, we stuty the Starobinsky-type inflation model in the framework of old-minimal supergravity, where the inflaton field in the original (non-supersymmetric) Starobinsky inflation model becomes a complex field. We study how the inflaton evolves on the two-dimensional field space, varying the initial condition. We show that (i) one of the scalar fields has a very steep potential once the trajectory is off from that of the original Starobinsky inflation, and that (ii) the $B$-mode signal observed by BICEP2 is too large to be consistent with the prediction of the model irrespective of the initial condition. Thus, the BICEP2 result strongly disfavors the complexified Starobinsky inflation in supergravity.

### Complexified Starobinsky Inflation in Supergravity in the Light of Recent BICEP2 Result [Cross-Listing]

Motivated by the recent observation of the $B$-mode signal in the cosmic microwave background by BICEP2, we stuty the Starobinsky-type inflation model in the framework of old-minimal supergravity, where the inflaton field in the original (non-supersymmetric) Starobinsky inflation model becomes a complex field. We study how the inflaton evolves on the two-dimensional field space, varying the initial condition. We show that (i) one of the scalar fields has a very steep potential once the trajectory is off from that of the original Starobinsky inflation, and that (ii) the $B$-mode signal observed by BICEP2 is too large to be consistent with the prediction of the model irrespective of the initial condition. Thus, the BICEP2 result strongly disfavors the complexified Starobinsky inflation in supergravity.