# Posts Tagged scalar field

## Recent Postings from scalar field

### Fermions in the 5D Gravity-Scalar Standing Wave Braneworld [Cross-Listing]

In the article we investigate localization problem for spinor fields within the 5D standing wave braneworld with the bulk real scalar field and show that there exist normalizable fermion field zero modes on the brane.

### On holography for (pseudo-)conformal cosmology [Cross-Listing]

We propose a holographic dual for (pseudo-)conformal cosmological scenario, with a scalar field that forms a moving domain wall in adS_5. The domain wall separates two vacua with unequal energy densities. Unlike in the existing construction, the 5d solution is regular in the relevant space-time domain.

### On holography for (pseudo-)conformal cosmology [Cross-Listing]

We propose a holographic dual for (pseudo-)conformal cosmological scenario, with a scalar field that forms a moving domain wall in adS_5. The domain wall separates two vacua with unequal energy densities. Unlike in the existing construction, the 5d solution is regular in the relevant space-time domain.

### On holography for (pseudo-)conformal cosmology

We propose a holographic dual for (pseudo-)conformal cosmological scenario, with a scalar field that forms a moving domain wall in adS_5. The domain wall separates two vacua with unequal energy densities. Unlike in the existing construction, the 5d solution is regular in the relevant space-time domain.

### Sphalerons and the Electroweak Phase Transition in Models with Higher Scalar Representations [Cross-Listing]

In this work we investigate the sphaleron solution in a $SU(2)\times U(1)_X$ gauge theory, which also encompasses the Standard Model, with higher scalar representation(s) ($J^{(i)},X^{(i)}$). We show that the field profiles describing the sphaleron in higher scalar multiplet, have similar trends like the doublet case with respect to the radial distance. We compute the sphaleron energy and find that it scales linearly with the vacuum expectation value of the scalar field and its slope depends on the representation. We also investigate the effect of $U(1)$ gauge field and find that it is small for the physical value of the mixing angle, $\theta_{W}$ and resembles the case for the doublet. For higher representations, we show that the criterion for strong first order phase transition, $v_{c}/T_{c}>\eta$, is relaxed with respect to the doublet case, i.e. $\eta<1$.

### Sphalerons and the Electroweak Phase Transition in Models with Higher Scalar Representations

In this work we investigate the sphaleron solution in a $SU(2)\times U(1)_X$ gauge theory, which also encompasses the Standard Model, with higher scalar representation(s) ($J^{(i)},X^{(i)}$). We show that the field profiles describing the sphaleron in higher scalar multiplet, have similar trends like the doublet case with respect to the radial distance. We compute the sphaleron energy and find that it scales linearly with the vacuum expectation value of the scalar field and its slope depends on the representation. We also investigate the effect of $U(1)$ gauge field and find that it is small for the physical value of the mixing angle, $\theta_{W}$ and resembles the case for the doublet. For higher representations, we show that the criterion for strong first order phase transition, $v_{c}/T_{c}>\eta$, is relaxed with respect to the doublet case, i.e. $\eta<1$.

### Dark Energy and Mass Generation

We consider a set of solutions for a massless quartic scalar field, recently devised, that satisfy a massive dispersion relation. We show that such solutions have the property to give the correct behavior for the equation of state of the dark energy. It seen that conformal invariance is restored and the mass gap goes to zero on a time scale determined by the Hubble constant and the strength of the self-interaction of the scalar field. When conformal invariance is restored, the equation of state for the dark energy can apply.

### Dark Energy and Mass Generation [Cross-Listing]

We consider a set of solutions for a massless quartic scalar field, recently devised, that satisfy a massive dispersion relation. We show that such solutions have the property to give the correct behavior for the equation of state of the dark energy. It seen that conformal invariance is restored and the mass gap goes to zero on a time scale determined by the Hubble constant and the strength of the self-interaction of the scalar field. When conformal invariance is restored, the equation of state for the dark energy can apply.

### Dark Energy and Mass Generation [Cross-Listing]

We consider a set of solutions for a massless quartic scalar field, recently devised, that satisfy a massive dispersion relation. We show that such solutions have the property to give the correct behavior for the equation of state of the dark energy. It seen that conformal invariance is restored and the mass gap goes to zero on a time scale determined by the Hubble constant and the strength of the self-interaction of the scalar field. When conformal invariance is restored, the equation of state for the dark energy can apply.

### Exact black hole formation in three dimensions [Cross-Listing]

We consider three dimensional Einstein gravity minimally/non-minimally coupled to a real scalar field with a self-interacting scalar potential and present the exact black hole formation in three dimensions. Firstly we obtain an exact time-dependent spherically symmetric solution in the non-minimal coupling model, describing the gravitational collapse to a scalar black hole at the infinite time, i.e. in the static limit. Then after taking a conformal transformation, we get the exact time-dependent solution in the minimal coupling model. The solutions can both only be asymptotically AdS because of the No-Go theorem in three dimensions which is resulted from the existence of a smooth black hole horizon. We also analyze their geometric properties and properties of the time evolution.

### Exact black hole formation in three dimensions

We consider three dimensional Einstein gravity minimally/non-minimally coupled to a real scalar field with a self-interacting scalar potential and present the exact black hole formation in three dimensions. Firstly we obtain an exact time-dependent spherically symmetric solution in the non-minimal coupling model, describing the gravitational collapse to a scalar black hole at the infinite time, i.e. in the static limit. Then after taking a conformal transformation, we get the exact time-dependent solution in the minimal coupling model. The solutions can both only be asymptotically AdS because of the No-Go theorem in three dimensions which is resulted from the existence of a smooth black hole horizon. We also analyze their geometric properties and properties of the time evolution.

### Non-linear Q-clouds around Kerr black holes

Q-balls are regular extended objects’ that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr) black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces – existence lines – of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q-clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q-cloud reduces to a linear cloud. Thus, Q-clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q-clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family.

### Non-linear Q-clouds around Kerr black holes [Cross-Listing]

Q-balls are regular extended objects’ that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr) black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces – existence lines – of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q-clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q-cloud reduces to a linear cloud. Thus, Q-clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q-clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family.

### Non-linear Q-clouds around Kerr black holes [Cross-Listing]

Q-balls are regular extended `objects’ that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr) black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces – existence lines – of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q-clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q-cloud reduces to a linear cloud. Thus, Q-clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q-clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family.

### The Effective Potential in Non-Conformal Gauge Theories

By using the renormalization group (RG) equation it has proved possible to sum logarithmic corrections to quantities that arise due to quantum effects in field theories. In particular, the effective potential V in the Standard Model in the limit that there are no massive parameters in the classical action (the "conformal limit") has been subject to this analysis, as has the effective potential in a scalar theory with a quartic self coupling and in massless scalar electrodynamics. Having multiple coupling constants and/or mass parameters in the initial action complicates this analysis, as then several mass scales arise. We show how to address this problem by considering the effective potential in scalar electrodynamics when the scalar field has a tree level mass term. In addition to summing logarithmic corrections by using the RG equation, we also consider the consequences of the condition V’(v)=0 where v is the vacuum expectation value of the scalar. If V is expanded in powers of the logarithms that arise, then it proves possible to show that either v is zero or that V is independent of the scalar. (That is, either there is no spontaneous symmetry breaking or the vacuum expectation value is not determined by minimizing V as V is "flat".)

### Inflation of small true vacuum bubble by quantization of Einstein-Hilbert action

We study the quantization of the Einstein-Hilbert action for a small true vacuum bubble without matter or scalar field. The quantization of action induces an extra term of potential called quantum potential in Hamilton-Jacobi equation, which gives expanding solutions including the exponential expansion solutions of the scalar factor $a$ for the bubble. We show that exponential expansion of the bubble continues with a short period (about a Planck time $t_p$), no matter whether the bubble is closed, flat or open. The exponential expansion ends spontaneously when the bubble becomes large, i.e., the scalar factor $a$ of the bubble approaches a Planck length $l_p$. We show that it is quantum potential of the small true vacuum bubble that plays the role of the scalar field potential suggested in the slow-roll inflation model. With the picture of quantum tunneling, we calculate particle creation rate during inflation, which shows that particles created by inflation have the capability of reheating the universe.

### Inflation of small true vacuum bubble by quantization of Einstein-Hilbert action [Cross-Listing]

We study the quantization of the Einstein-Hilbert action for a small true vacuum bubble without matter or scalar field. The quantization of action induces an extra term of potential called quantum potential in Hamilton-Jacobi equation, which gives expanding solutions including the exponential expansion solutions of the scalar factor $a$ for the bubble. We show that exponential expansion of the bubble continues with a short period (about a Planck time $t_p$), no matter whether the bubble is closed, flat or open. The exponential expansion ends spontaneously when the bubble becomes large, i.e., the scalar factor $a$ of the bubble approaches a Planck length $l_p$. We show that it is quantum potential of the small true vacuum bubble that plays the role of the scalar field potential suggested in the slow-roll inflation model. With the picture of quantum tunneling, we calculate particle creation rate during inflation, which shows that particles created by inflation have the capability of reheating the universe.

### Inflation of small true vacuum bubble by quantization of Einstein-Hilbert action [Cross-Listing]

We study the quantization of the Einstein-Hilbert action for a small true vacuum bubble without matter or scalar field. The quantization of action induces an extra term of potential called quantum potential in Hamilton-Jacobi equation, which gives expanding solutions including the exponential expansion solutions of the scalar factor $a$ for the bubble. We show that exponential expansion of the bubble continues with a short period (about a Planck time $t_p$), no matter whether the bubble is closed, flat or open. The exponential expansion ends spontaneously when the bubble becomes large, i.e., the scalar factor $a$ of the bubble approaches a Planck length $l_p$. We show that it is quantum potential of the small true vacuum bubble that plays the role of the scalar field potential suggested in the slow-roll inflation model. With the picture of quantum tunneling, we calculate particle creation rate during inflation, which shows that particles created by inflation have the capability of reheating the universe.

### Inflation of small true vacuum bubble by quantization of Einstein-Hilbert action [Cross-Listing]

We study the quantization of the Einstein-Hilbert action for a small true vacuum bubble without matter or scalar field. The quantization of action induces an extra term of potential called quantum potential in Hamilton-Jacobi equation, which gives expanding solutions including the exponential expansion solutions of the scalar factor $a$ for the bubble. We show that exponential expansion of the bubble continues with a short period (about a Planck time $t_p$), no matter whether the bubble is closed, flat or open. The exponential expansion ends spontaneously when the bubble becomes large, i.e., the scalar factor $a$ of the bubble approaches a Planck length $l_p$. We show that it is quantum potential of the small true vacuum bubble that plays the role of the scalar field potential suggested in the slow-roll inflation model. With the picture of quantum tunneling, we calculate particle creation rate during inflation, which shows that particles created by inflation have the capability of reheating the universe.

### Parametric Resonance of Entropy Perturbations in Massless Preheating

Here, we revisit the question of possible preheating of entropy modes in a two field model with a massless inflaton coupled to a matter scalar field. Using a perturbative approximation to the covariant method we demonstrate that there is indeed a parametric instability of the entropy mode which then at second order leads to exponential growth of the curvature fluctuation on super-Hubble scale. Back-reaction effects shut off the induced curvature fluctuations, but only after their amplitude has grown to a phenomenologically unacceptable value. This confirms previous results obtained using different methods.

### Parametric Resonance of Entropy Perturbations in Massless Preheating [Cross-Listing]

Here, we revisit the question of possible preheating of entropy modes in a two field model with a massless inflaton coupled to a matter scalar field. Using a perturbative approximation to the covariant method we demonstrate that there is indeed a parametric instability of the entropy mode which then at second order leads to exponential growth of the curvature fluctuation on super-Hubble scale. Back-reaction effects shut off the induced curvature fluctuations, but only after their amplitude has grown to a phenomenologically unacceptable value. This confirms previous results obtained using different methods.

### Parametric Resonance of Entropy Perturbations in Massless Preheating [Cross-Listing]

Here, we revisit the question of possible preheating of entropy modes in a two field model with a massless inflaton coupled to a matter scalar field. Using a perturbative approximation to the covariant method we demonstrate that there is indeed a parametric instability of the entropy mode which then at second order leads to exponential growth of the curvature fluctuation on super-Hubble scale. Back-reaction effects shut off the induced curvature fluctuations, but only after their amplitude has grown to a phenomenologically unacceptable value. This confirms previous results obtained using different methods.

### Parametric Resonance of Entropy Perturbations in Massless Preheating [Cross-Listing]

Here, we revisit the question of possible preheating of entropy modes in a two field model with a massless inflaton coupled to a matter scalar field. Using a perturbative approximation to the covariant method we demonstrate that there is indeed a parametric instability of the entropy mode which then at second order leads to exponential growth of the curvature fluctuation on super-Hubble scale. Back-reaction effects shut off the induced curvature fluctuations, but only after their amplitude has grown to a phenomenologically unacceptable value. This confirms previous results obtained using different methods.

### Disformal transformation of cosmological perturbations

We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar-tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar-tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (non)conservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame.

### Disformal transformation of cosmological perturbations [Cross-Listing]

We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar-tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar-tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (non)conservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame.

### Why is the Dark Axion Mass $10^{-22}$ eV? [Cross-Listing]

Scalar field dark matter likely is able to solve all small-scale cosmology problems facing the cold dark matter (CDM), and has become an emerging contender to challenge the CDM. It however requires a particle mass $\sim 1 – 2 \times10^{-22}$eV. We find such an extremely small particle mass can naturally arise from a non-QCD axion mechanism, under fairly general assumptions that a few species of self-interacting light particles of comparable masses and a massless gauge boson decouple from the bright sector since the photon temperature exceeds 200 GeV, and the axion is the dominant dark matter. These assumptions also set the axion decay constant scale to several $\times 10^{16}$ GeV. Given the above axion mass range, we further pin down the dark-sector particles to consist of only one species of fermion and anti-fermion, likely right-handed neutrinos. With a mass around $92-128$ eV, the dark-sector particles may constitute a minority population of dark matter. If the gauge boson lives on SU(2), a dilute instanton gas can contribute about $2.5\%$ of the total relativistic relics in the cosmic microwave background radiation.

### An Alternative to Particle Dark Matter [Cross-Listing]

We propose an alternative to particle dark matter that borrows ingredients of MOdified Newtonian Dynamics (MOND) while adding new key components. The first new feature is a dark matter fluid, in the form of a scalar field with small equation of state and sound speed. This component is critical in reproducing the success of cold dark matter for the expansion history and the growth of linear perturbations, but does not cluster significantly on non-linear scales. Instead, the missing mass problem on non-linear scales is addressed by a modification of the gravitational force law. The force law approximates MOND at large and intermediate accelerations, and therefore reproduces the empirical success of MOND at fitting galactic rotation curves. At ultra-low accelerations, the force law reverts to an inverse-square-law, albeit with a larger Newton’s constant. This latter regime is important in galaxy clusters and is consistent with their observed isothermal profiles. We present an explicit relativistic theory in terms of two scalar fields. The first scalar field is governed by a Dirac-Born-Infeld action and behaves as a dark matter fluid on large scales. The second scalar field also has single-derivative interactions and mediates a fifth force that modifies gravity on non-linear scales. Both scalars are coupled to matter via an effective metric that depends locally on the fields. The form of this effective metric implies the equality of the two scalar gravitational potentials, which ensures that lensing and dynamical mass estimates agree.

### An Alternative to Particle Dark Matter [Cross-Listing]

We propose an alternative to particle dark matter that borrows ingredients of MOdified Newtonian Dynamics (MOND) while adding new key components. The first new feature is a dark matter fluid, in the form of a scalar field with small equation of state and sound speed. This component is critical in reproducing the success of cold dark matter for the expansion history and the growth of linear perturbations, but does not cluster significantly on non-linear scales. Instead, the missing mass problem on non-linear scales is addressed by a modification of the gravitational force law. The force law approximates MOND at large and intermediate accelerations, and therefore reproduces the empirical success of MOND at fitting galactic rotation curves. At ultra-low accelerations, the force law reverts to an inverse-square-law, albeit with a larger Newton’s constant. This latter regime is important in galaxy clusters and is consistent with their observed isothermal profiles. We present an explicit relativistic theory in terms of two scalar fields. The first scalar field is governed by a Dirac-Born-Infeld action and behaves as a dark matter fluid on large scales. The second scalar field also has single-derivative interactions and mediates a fifth force that modifies gravity on non-linear scales. Both scalars are coupled to matter via an effective metric that depends locally on the fields. The form of this effective metric implies the equality of the two scalar gravitational potentials, which ensures that lensing and dynamical mass estimates agree.

### An Alternative to Particle Dark Matter

We propose an alternative to particle dark matter that borrows ingredients of MOdified Newtonian Dynamics (MOND) while adding new key components. The first new feature is a dark matter fluid, in the form of a scalar field with small equation of state and sound speed. This component is critical in reproducing the success of cold dark matter for the expansion history and the growth of linear perturbations, but does not cluster significantly on non-linear scales. Instead, the missing mass problem on non-linear scales is addressed by a modification of the gravitational force law. The force law approximates MOND at large and intermediate accelerations, and therefore reproduces the empirical success of MOND at fitting galactic rotation curves. At ultra-low accelerations, the force law reverts to an inverse-square-law, albeit with a larger Newton’s constant. This latter regime is important in galaxy clusters and is consistent with their observed isothermal profiles. We present an explicit relativistic theory in terms of two scalar fields. The first scalar field is governed by a Dirac-Born-Infeld action and behaves as a dark matter fluid on large scales. The second scalar field also has single-derivative interactions and mediates a fifth force that modifies gravity on non-linear scales. Both scalars are coupled to matter via an effective metric that depends locally on the fields. The form of this effective metric implies the equality of the two scalar gravitational potentials, which ensures that lensing and dynamical mass estimates agree.

### An Alternative to Particle Dark Matter [Cross-Listing]

We propose an alternative to particle dark matter that borrows ingredients of MOdified Newtonian Dynamics (MOND) while adding new key components. The first new feature is a dark matter fluid, in the form of a scalar field with small equation of state and sound speed. This component is critical in reproducing the success of cold dark matter for the expansion history and the growth of linear perturbations, but does not cluster significantly on non-linear scales. Instead, the missing mass problem on non-linear scales is addressed by a modification of the gravitational force law. The force law approximates MOND at large and intermediate accelerations, and therefore reproduces the empirical success of MOND at fitting galactic rotation curves. At ultra-low accelerations, the force law reverts to an inverse-square-law, albeit with a larger Newton’s constant. This latter regime is important in galaxy clusters and is consistent with their observed isothermal profiles. We present an explicit relativistic theory in terms of two scalar fields. The first scalar field is governed by a Dirac-Born-Infeld action and behaves as a dark matter fluid on large scales. The second scalar field also has single-derivative interactions and mediates a fifth force that modifies gravity on non-linear scales. Both scalars are coupled to matter via an effective metric that depends locally on the fields. The form of this effective metric implies the equality of the two scalar gravitational potentials, which ensures that lensing and dynamical mass estimates agree.

### Extremal Hairy Black Holes

We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and an U(1) electromagnetic field. Solving the coupled Einstein-Maxwell-scalar system we find exact hairy charged black hole solutions with the scalar field regular everywhere. We go to the zero temperature limit and we study the effect of the scalar field on the near horizon geometry of an extremal black hole. We find that except a critical value of the charge of the black hole there is also a critical value of the charge of the scalar field beyond of which the extremal black hole is destabilized. We study the thermodynamics of these solutions and we find that if the space is flat then at low temperature the Reissner-Nordstr\"om black hole is thermodynamically preferred, while if the space is AdS the hairy charged black hole is thermodynamically preferred at low temperature.

### Extremal Hairy Black Holes [Cross-Listing]

We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and an U(1) electromagnetic field. Solving the coupled Einstein-Maxwell-scalar system we find exact hairy charged black hole solutions with the scalar field regular everywhere. We go to the zero temperature limit and we study the effect of the scalar field on the near horizon geometry of an extremal black hole. We find that except a critical value of the charge of the black hole there is also a critical value of the charge of the scalar field beyond of which the extremal black hole is destabilized. We study the thermodynamics of these solutions and we find that if the space is flat then at low temperature the Reissner-Nordstr\"om black hole is thermodynamically preferred, while if the space is AdS the hairy charged black hole is thermodynamically preferred at low temperature.

### Hadamard renormalized scalar field theory on anti-de Sitter space-time

We consider a real massive free quantum scalar field with arbitrary curvature coupling on $n$-dimensional anti-de Sitter space-time. We use Hadamard renormalization to find the vacuum expectation values of the quadratic field fluctuations and the stress-energy tensor, presenting explicit results for $n=2$ to $n=11$ inclusive.

### Geodesic structure of Janis-Newman-Winicour space-time

In the present paper we study the geodesic structure of the Janis-Newman-Winicour(JNW) space-time which contains a strong curvature naked singularity. This metric is an extension of the Schwarzschild geometry when a massless scalar field is included. We find that the strength parameter $\mu$ of the scalar field effects on the geodesic structure of the JNW space-time. By solving the geodesic equation and analyzing the behavior of effective potential, we investigate all geodesic types of the test particle and the photon in the JNW space-time. At the same time we simulate all the geodesic orbits corresponding to the energy levels of the effective potential in the JNW space-time.

### Higher Order Lagrangians inspired in the Pais-Uhlenbeck Oscillator and their cosmological applications [Cross-Listing]

We study higher derivative terms associated to an scalar field cosmology. We consider a coupling between the scalar field and the geometry inspired in the Pais-Uhlenbeck oscillator given by $\alpha\partial_{\mu}\partial^{\mu}\phi\partial_{\nu}\partial^{\nu}\phi.$ We investigate the cosmological dynamics in a phase space. For $\alpha>0$ we provide conditions for the stability of de Sitter solutions. For $\alpha<0,$ which is the portion of the parameter space where the crossing of the phantom divide $w_{DE}=-1$ and the cyclic behavior are possible, we present regions in the parameter space where the ghost has benign or malicious behavior, according to Smilga’s classification.

### Higher Order Lagrangians inspired in the Pais-Uhlenbeck Oscillator and their cosmological applications

We study higher derivative terms associated to an scalar field cosmology. We consider a coupling between the scalar field and the geometry inspired in the Pais-Uhlenbeck oscillator given by $\alpha\partial_{\mu}\partial^{\mu}\phi\partial_{\nu}\partial^{\nu}\phi.$ We investigate the cosmological dynamics in a phase space. For $\alpha>0$ we provide conditions for the stability of de Sitter solutions. For $\alpha<0,$ which is the portion of the parameter space where the crossing of the phantom divide $w_{DE}=-1$ and the cyclic behavior are possible, we present regions in the parameter space where the ghost has benign or malicious behavior, according to Smilga’s classification.

### Higher Order Lagrangians inspired in the Pais-Uhlenbeck Oscillator and their cosmological applications [Cross-Listing]

We study higher derivative terms associated to an scalar field cosmology. We consider a coupling between the scalar field and the geometry inspired in the Pais-Uhlenbeck oscillator given by $\alpha\partial_{\mu}\partial^{\mu}\phi\partial_{\nu}\partial^{\nu}\phi.$ We investigate the cosmological dynamics in a phase space. For $\alpha>0$ we provide conditions for the stability of de Sitter solutions. For $\alpha<0,$ which is the portion of the parameter space where the crossing of the phantom divide $w_{DE}=-1$ and the cyclic behavior are possible, we present regions in the parameter space where the ghost has benign or malicious behavior, according to Smilga’s classification.

### Myers-Perry black holes with scalar hair and a mass gap [Cross-Listing]

We construct a family of asymptotically flat, rotating black holes with scalar hair and a regular horizon, within five dimensional Einstein’s gravity minimally coupled to a complex, massive scalar field doublet. These solutions are supported by rotation and have no static limit. They are described by their mass $M$, two equal angular momenta $J_1=J_2\equiv J$ and a conserved Noether charge $Q$, measuring the scalar hair. For vanishing horizon size the solutions reduce to five dimensional boson stars. In the limit of vanishing Noether charge density, the scalar field becomes point-wise arbitrarily small and the geometry becomes, locally, arbitrarily close to that of a specific set of Myers-Perry black holes (MPBHs); but there remains a global difference with respect to the latter, manifest in a finite mass gap. Thus, the scalar hair never becomes a linear perturbation of MPBHs. This is a qualitative difference when compared to Kerr black holes with scalar hair~\cite{Herdeiro:2014goa}. Whereas the existence of the latter can be anticipated in linear theory, from the existence of scalar bound states on the Kerr geometry (i.e. scalar clouds), the hair of these MPBHs is intrinsically non-linear.

### Myers-Perry black holes with scalar hair and a mass gap

We construct a family of asymptotically flat, rotating black holes with scalar hair and a regular horizon, within five dimensional Einstein’s gravity minimally coupled to a complex, massive scalar field doublet. These solutions are supported by rotation and have no static limit. They are described by their mass $M$, two equal angular momenta $J_1=J_2\equiv J$ and a conserved Noether charge $Q$, measuring the scalar hair. For vanishing horizon size the solutions reduce to five dimensional boson stars. In the limit of vanishing Noether charge density, the scalar field becomes point-wise arbitrarily small and the geometry becomes, locally, arbitrarily close to that of a specific set of Myers-Perry black holes (MPBHs); but there remains a global difference with respect to the latter, manifest in a finite mass gap. Thus, the scalar hair never becomes a linear perturbation of MPBHs. This is a qualitative difference when compared to Kerr black holes with scalar hair~\cite{Herdeiro:2014goa}. Whereas the existence of the latter can be anticipated in linear theory, from the existence of scalar bound states on the Kerr geometry (i.e. scalar clouds), the hair of these MPBHs is intrinsically non-linear.

### Emergent Cosmology, Inflation and Dark Energy from Spontaneous Breaking of Scale Invariance [Cross-Listing]

A new class of gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold are studied in some detail. These models involve an additional R^2 (square of the scalar curvature) term as well as scalar matter field potentials of appropriate form so that the pertinent action is invariant under global Weyl-scale symmetry. Scale invariance is spontaneously broken upon integration of the equations of motion. After performing transition to the physical Einstein frame we obtain: (i) An effective potential for the scalar field with two flat regions which allows for a unified description of both early universe inflation as well as of present dark energy epoch; (ii) For a definite parameter range the model possesses a non-singular "emergent universe" solution which describes an initial phase of evolution that precedes the inflationary phase.

### Emergent Cosmology, Inflation and Dark Energy from Spontaneous Breaking of Scale Invariance [Replacement]

A new class of gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold are studied in some detail. These models involve an additional R^2 (square of the scalar curvature) term as well as scalar matter field potentials of appropriate form so that the pertinent action is invariant under global Weyl-scale symmetry. Scale invariance is spontaneously broken upon integration of the equations of motion. After performing transition to the physical Einstein frame we obtain: (i) An effective potential for the scalar field with two flat regions which allows for a unified description of both early universe inflation as well as of present dark energy epoch; (ii) For a definite parameter range the model possesses a non-singular "emergent universe" solution which describes an initial phase of evolution that precedes the inflationary phase.

### Emergent Cosmology, Inflation and Dark Energy from Spontaneous Breaking of Scale Invariance [Replacement]

A new class of gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold are studied in some detail. These models involve an additional R^2 (square of the scalar curvature) term as well as scalar matter field potentials of appropriate form so that the pertinent action is invariant under global Weyl-scale symmetry. Scale invariance is spontaneously broken upon integration of the equations of motion. After performing transition to the physical Einstein frame we obtain: (i) An effective potential for the scalar field with two flat regions which allows for a unified description of both early universe inflation as well as of present dark energy epoch; (ii) For a definite parameter range the model possesses a non-singular "emergent universe" solution which describes an initial phase of evolution that precedes the inflationary phase.

### Emergent Cosmology, Inflation and Dark Energy from Spontaneous Breaking of Scale Invariance

A new class of gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold are studied in some detail. These models involve an additional R^2 (square of the scalar curvature) term as well as scalar matter field potentials of appropriate form so that the pertinent action is invariant under global Weyl-scale symmetry. Scale invariance is spontaneously broken upon integration of the equations of motion. After performing transition to the physical Einstein frame we obtain: (i) An effective potential for the scalar field with two flat regions which allows for a unified description of both early universe inflation as well as of present dark energy epoch; (ii) For a definite parameter range the model possesses a non-singular "emergent universe" solution which describes an initial phase of evolution that precedes the inflationary phase.

### Bouncing scalar field cosmology in the polymeric minisuperspace picture

We study a cosmological setup consisting of a FRW metric as the background geometry with a massless scalar field in the framework of classical polymerization of a given dynamical system. To do this, we first introduce the polymeric representation of the quantum operators. We then extend the corresponding process to reach a transformation which maps any classical variable to its polymeric counterpart. It is shown that such a formalism has also an analogue in terms of the symplectic structure, i.e., instead of applying polymerization to the classical Hamiltonian to arrive its polymeric form, one can use a new set of variables in terms of which Hamiltonian retains its form but now the corresponding symplectic structure gets a new deformed functional form. We show that these two methods are equivalent and by applying of them to the scalar field FRW cosmology see that the resulting scale factor exhibits a bouncing behavior from a contraction phase to an expanding era. Since the replacing of the big bang singularity by a bouncing behavior is one of the most important predictions of the quantum cosmological theories, we may claim that our polymerized classical model brings with itself some signals from quantum theory.

### Combined cosmological tests of a bivalent tachyonic dark energy scalar field model

A recently investigated tachyonic scalar field dark energy dominated universe exhibits a bivalent future: depending on initial parameters can run either into a de Sitter exponential expansion or into a traversable future soft singularity followed by a contraction phase. We also include in the model (i) a tiny amount of radiation, (ii) baryonic matter ($\Omega _{b}h^{2}=0.022161$, where the Hubble constant is fixed as $h=0.706$) and (iii) cold dark matter (CDM). Out of a variety of six types of evolutions arising in a more subtle classification, we identify two in which in the past the scalar field effectively degenerates into a dust (its pressure drops to an insignificantly low negative value). These are the evolutions of type IIb converging to de Sitter and type III hitting the future soft singularity. We confront these background evolutions with various cosmological tests, including the supernova type Ia Union 2.1 data, baryon acoustic oscillation distance ratios, the $Omh^{2}$ diagnostic and the cosmic microwave background (CMB) acoustic scale. We determine a subset of the evolutions of both types which at 1$\sigma$ confidence level are consistent with all of these cosmological tests. At perturbative level we derive the CMB temperature power spectrum to find the best agreement with the Planck data for $\Omega _{CDM}=0.22$. The fit is as good as for the $\Lambda$CDM model at high multipoles, but the power remains slightly overestimated at low multipoles, for both types of evolutions. The rest of the CDM is effectively generated by the tachyonic field, which in this sense acts as a combined dark energy and dark matter model.

### Combined cosmological tests of a bivalent tachyonic dark energy scalar field model [Cross-Listing]

A recently investigated tachyonic scalar field dark energy dominated universe exhibits a bivalent future: depending on initial parameters can run either into a de Sitter exponential expansion or into a traversable future soft singularity followed by a contraction phase. We also include in the model (i) a tiny amount of radiation, (ii) baryonic matter ($\Omega _{b}h^{2}=0.022161$, where the Hubble constant is fixed as $h=0.706$) and (iii) cold dark matter (CDM). Out of a variety of six types of evolutions arising in a more subtle classification, we identify two in which in the past the scalar field effectively degenerates into a dust (its pressure drops to an insignificantly low negative value). These are the evolutions of type IIb converging to de Sitter and type III hitting the future soft singularity. We confront these background evolutions with various cosmological tests, including the supernova type Ia Union 2.1 data, baryon acoustic oscillation distance ratios, the $Omh^{2}$ diagnostic and the cosmic microwave background (CMB) acoustic scale. We determine a subset of the evolutions of both types which at 1$\sigma$ confidence level are consistent with all of these cosmological tests. At perturbative level we derive the CMB temperature power spectrum to find the best agreement with the Planck data for $\Omega _{CDM}=0.22$. The fit is as good as for the $\Lambda$CDM model at high multipoles, but the power remains slightly overestimated at low multipoles, for both types of evolutions. The rest of the CDM is effectively generated by the tachyonic field, which in this sense acts as a combined dark energy and dark matter model.

### Dynamic C-metrics in (Gauged) Supergravities

We construct an exact time-dependent charged dilaton C-metric in four-dimensional ${\cal N}=4$ gauged supergravity. The scalar field drives the time evolution by transferring energy to the black holes, thereby causing their masses to increase and their acceleration to decrease. The values of the electric/magnetic and scalar charges determine three regions of potential time evolution. This solution holographically describes a strongly-coupled three-dimensional conformal field theory on the background of an evolving black hole. We also find new static charged dilaton C-metrics, which arise in four-dimensional Einstein-Maxwell-dilaton theories whose scalar potential can be expressed in terms of a superpotential.

### Varying-Alpha and K-Essence [Cross-Listing]

We introduce a model which allows the fine structure constant (alpha) to vary throughout space and time due to a coupling to a scalar field with a non-canonical kinetic structure. This provided a new extension of the Bekenstein-Sandvik-Barrow-Magueijo model of alpha variations. The background cosmology is studied in detail using dynamical systems techniques for a scalar field of ghost condensate type. We show generically that if the kinetic terms are chosen to allow an accelerated late-time attractor for the expansion scale factor then alpha will not asymptote to a constant at late times.

### Varying-Alpha and K-Essence

We introduce a model which allows the fine structure constant (alpha) to vary throughout space and time due to a coupling to a scalar field with a non-canonical kinetic structure. This provided a new extension of the Bekenstein-Sandvik-Barrow-Magueijo model of alpha variations. The background cosmology is studied in detail using dynamical systems techniques for a scalar field of ghost condensate type. We show generically that if the kinetic terms are chosen to allow an accelerated late-time attractor for the expansion scale factor then alpha will not asymptote to a constant at late times.

### Varying-Alpha and K-Essence [Cross-Listing]

We introduce a model which allows the fine structure constant (alpha) to vary throughout space and time due to a coupling to a scalar field with a non-canonical kinetic structure. This provided a new extension of the Bekenstein-Sandvik-Barrow-Magueijo model of alpha variations. The background cosmology is studied in detail using dynamical systems techniques for a scalar field of ghost condensate type. We show generically that if the kinetic terms are chosen to allow an accelerated late-time attractor for the expansion scale factor then alpha will not asymptote to a constant at late times.