With the usual definitions for the entropy and the temperature associated with the apparent horizon, we show that the unified first law on the apparent horizon is equivalent to the Friedmann equation for the scalar--tensor theory with non-minimally derivative coupling. The second law of thermodynamics on the apparent horizon is also satisfied. The results support a deep and fundamental connection between gravitation, thermodynamics, and quantum theory.
We perform a dynamical analysis for the exponential scalar field with non-minimally derivative coupling. For the quintessence case, the stable fixed points are the same with and without the non-minimally derivative coupling. For the phantom case, the attractor with dark energy domination exists for the minimal coupling only. For the non-minimally derivative coupling without the standard canonical kinetic term, only the de-Sitter attractor exists, and the dark matter solution is unstable.
We revisit the analogy between a minimally coupled scalar field in general relativity and a perfect fluid, correcting previous identifications of effective temperature and chemical potential. This provides a useful complementary picture for the first-order thermodynamics of scalar-tensor gravity, paving the way for the Einstein frame formulation (which eluded previous attempts) and raises interesting questions to further develop the analogy.
We derive the general formulae for the the scalar and tensor spectral tilts to the second order for the inflationary models with non-minimally derivative coupling without taking the high friction limit. The non-minimally kinetic coupling to Einstein tensor brings the energy scale in the inflationary models down to be sub-Planckian. In the high friction limit, the Lyth bound is modified with an extra suppression factor, so that the field excursion of the inflaton is sub-Planckian. The inflationary models with non-minimally derivative coupling are more consistent with observations in the high fr…
We construct higher-derivative gravities with a non-minimally coupled Maxwell field. The Lagrangian consists of polynomial invariants built from the Riemann tensor and the Maxwell field strength in such a way that the equations of motion are second order for both the metric and the Maxwell potential. We also generalize the construction to involve a generic non-minimally coupled $p$-form field strength. We then focus on one low-lying example in four dimensions and construct the exact magnetically-charged black holes. We also construct exact electrically-charged $z=2$ Lifshitz black holes. We ob…
We investigate whether the gravitational thermodynamic properties of the scalar-tensor theory of gravity are affected by the conformal transformation or not. As an explicit example, we consider an electrically charged static spherical black hole in the 4-dimensional low energy effective theory of bosonic string.
With the usual definitions for the entropy and the temperature associated with the apparent horizon, we discuss the first law of the thermodynamics on the apparent in the general scalar-tensor theory of gravity with the kinetic term of the scalar field non-minimally coupling to Einstein tensor. We show the equivalence between the first law of thermodynamics on the apparent horizon and Friedmann equation for the general models, by using a mass-like function which is equal to the Misner-Sharp mass on the apparent horizon. The results further support the universal relationship between the first l…
We study asymptotic safety of models of the higher derivative quantum gravity with and without matter. The beta functions are derived by utilizing the functional renormalization group, and non-trivial fixed points are found. It turns out that all couplings in gravity sector, namely the cosmological constant, the Newton constant, and the $R^2$ and $R_{μν}^2$ coupling constants, are relevant in case of higher derivative pure gravity. For the Higgs-Yukawa model non-minimal coupled with higher derivative gravity, we find a stable fixed point at which the scalar-quartic and the Yukawa coupling cons…
The scalar-spinor interaction Lagrangian is presented by the Yukawa potential. In dS ambient space formalism, the interaction Lagrangian of scalar-spinor fields was obtained from a new transformation which is very similar to the guage theory. The interaction of massless minimally coupled scalar and spinor fields was investigated. The Minkowski limit of the massless minimally coupled scalar field and massive spinor field interaction in the ambient space formalism of de Sitter space time is calculated. The interaction Lagrangian and massless minimally coupled scalar field in the null curvature l…
We use Noether symmetry approach to find spherically symmetric static solutions of the non-minimally coupled electromagnetic fields to gravity. We construct the point-like Lagrangian under the spherical symmetry assumption. Then we determine Noether symmetry and the corresponding conserved charge. We derive Euler-Lagrange equations from this point-like Lagrangian and show that these equations are same with the differential equations derived from the field equations of the model. Also we give two new exact asymptotically flat solutions to these equations and investigate some thermodynamic prope…
We study a nonminimal derivative inflationary model in the presence of the Gauss-Bonnet term. To have a complete treatment of the model, we consider a general form of the nonminimal derivative function and also the Gauss-Bonnet coupling term. By following the ADM formalism, expanding the action up to the third order in the perturbations and using the correlation functions, we study the perturbation and its non-Gaussian feature in details. We also study the consistency relation that gets modified in the presence of the Gauss-Bonnet term in the action. We compare the results of our consideration…
In this work we investigate the evolution of a Universe consisted of a scalar field, a dark matter field and non-interacting baryonic matter and radiation. The scalar field, which plays the role of dark energy, is non-minimally coupled to space-time curvature, and drives the Universe to a present accelerated expansion. The non-relativistic dark matter field interacts directly with the dark energy and has a pressure which follows from a thermodynamic theory. We show that this model can reproduce the expected behavior of the density parameters, deceleration parameter and luminosity distance.
By using the 't Hooft "brick wall" model and the Pauli-Villars regularization scheme we calculate the statistical-mechanical entropy arising from the minimally coupled scalar fields which rotate with the azimuthal angular velocity $Ω_0=Ω_H$ ($Ω_H$ is the angular velocity of the black hole horizon) in the general four-dimensional non-extreme stationary axisymmetric black hole space-time. We also show, for the Kerr-Newman and the Einstein-Maxwell dilaton-axion black holes, that the statistical-mechanical entropy obtained from our derivation and the quantum thermodynamical entropy by the conical …
We investigate higher-derivative extensions of Einstein-Maxwell theory that are invariant under electromagnetic duality rotations, allowing for non-minimal couplings between gravity and the gauge field. Working in a derivative expansion of the action, we characterize the Lagrangians giving rise to duality-invariant theories up to the eight-derivative level, providing the complete list of operators that one needs to include in the action. We also characterize the set of duality-invariant theories whose action is quadratic in the Maxwell field strength but which are non-minimally coupled to the …
We construct a single scalar field model with tachyon field non-minimally coupled to itself, its derivative and to the curvature. We study the cosmological dynamics of the equation of state in this setup. While it is expected that in the case of single scalar field the crossing of the phantom divide line can not be realized [10], we show that incorporating quantum corrections, namely, non-minimal derivative coupling of scalar field with curvature in our model, lead to phantom divide crossing.
We present consistent supersymmetric theories invariant under the generalization of the Galilean shift symmetry to ${\cal{N}}=1$ superspace. These theories are constructed via the decoupling limit of certain non-minimally derivative coupled supergravities, thus they correspond to the supersymmetrization of the so-called covariant Galileon. Specifically, these theories are constructed in the linearized ${\cal{N}}=1$ new-minimal supergravity set-up where the chiral supermultiplet is minimally coupled to gravity via the standard R-current contact term, and, at the same time, non-minimally derivat…
We investigate the quasinormal modes of a test massless, minimally coupled scalar field on a static and spherically symmetric black hole in the scalar-tensor theory with field derivative coupling to the Einstein tensor, which is a part of the Horndeski theory with the shift symmetry. In our solution, the spacetime is asymptotically AdS (anti-de Sitter), where the effective AdS curvature scale is determined solely by the derivative coupling constant. The metric approaches the AdS spacetime in the asymptotic infinity limit and precisely recovers the Schwarzschild-AdS solution in general relativi…
We study the quasi-normal modes of asymptotically anti-de Sitter black holes in a class of shift-symmetric Horndeski theories where a gravitational scalar is derivatively coupled to the Einstein tensor. The space-time differs from exact Schwarzschild-anti-de Sitter, resulting in a different effective potential for the quasi-normal modes and a different spectrum. We numerically compute this spectrum for a massless test scalar coupled both minimally to the metric, and non-minimally to the gravitational scalar. We find interesting differences from the Schwarzschild-anti-de Sitter black hole found…
In this work it is investigated the evolution of a Universe where a scalar field, non-minimally coupled to space-time curvature, plays the role of quintessence and drives the Universe to a present accelerated expansion. A non-relativistic dark matter constituent that interacts directly with dark energy is also considered, where the dark matter particle mass is assumed to be proportional to the value of the scalar field. Two models for dark matter pressure are considered: the usual one, pressureless, and another that comes from a thermodynamic theory and relates the pressure with the coupling b…
The main concepts of general relativistic thermodynamics and general relativistic statistical mechanics are reviewed. The main building block of the proper relativistic extension of the classical thermodynamics laws is the four-temperature vector β, which plays a major role in the quantum framework and defines a very convenient hydrodynamic frame. The general relativistic thermodynamic equilibrium condition demands βto be a Killing vector field. We show that a remarkable consequence is that all Lie derivatives of all physical observables along the four-temperature flow must then vanish.
A detailed and updated review is given of De Filippo's Non-unitary $4$-th Derivative Gravity and its Newtonian limit, by pointing out the crucial role of non-unitarity in addressing transition to classicality and specifically localization of macroscopic bodies, microscopic foundation of the second law of thermodynamics, measurement problem; furthermore it provides a quantum field theory of gravity possibly not only renormalizable but even finite, with a cancelation mechanism analogous to supersymmetric field theories where cancelations are due to superpartners whereas here to negative energy f…
An exact four-dimensional black hole solution of gravity with a minimally coupled self-interacting scalar field is reported. The event horizon is a surface of negative constant curvature enclosing the curvature singularity at the origin, and the scalar field is regular everywhere outside the origin. This solution is an asymptotically locally AdS spacetime. The strong energy condition is satisfied on and outside the event horizon. The thermodynamical analysis shows the existence of a critical temperature, below which a black hole in vacuum undergoes a spontaneous dressing up with a nontrivial s…
When we consider five-dimensional warped Taub-NUT/Bolt AdS black string with minimally coupled massive scalar field, we calculate entropy by using the brick wall method. It is found that they are proportional to being quadratically divergent in a cutoff parameter. In particular, we show that the entropy of warped Taub-NUT AdS black string holds for an area law in the bulk as well as on the brane. Furthermore, when the negative cosmological constant is treated as thermodynamic pressure, we calculate the thermodynamic quantities and investigate their extended thermodynamic properties. Interestin…
In this note, we examine the scattering of two identical fermions in theories where fermionic fields minimally coupled to higher derivative gravity. In particular, we consider the extension of general relativity with $R^2$ corrections or non-local terms. We expand the action of fermions around the flat space background and obtain two fermion-one graviton vertex. Then, by considering the scattering amplitude of two fermions, we calculate the non-relativistic limit and that obtain the potential for two fermion-fermion interaction which would be the usual Newtonian potential corrected with a Yuka…
We perform a full investigation on dynamics of a new dark energy model in which the four-derivative of a non-canonical scalar field (tachyon) is non-minimally coupled to the vector torsion. Our analysis is done in the framework of teleparallel equivalent of general relativity which is based on torsion instead of curvature. We show that in our model there exists a late-time scaling attractor (point $P_{4}$), corresponding to an accelerating universe with the property that dark energy and dark matter densities are of the same order. Such a point can help to alleviate the cosmological coincidence…
A linear relationship between the Hubble expansion parameter and the time derivative of the scalar field is assumed in order to derive exact analytic cosmological solutions to Einstein's gravity with two fluids: a barotropic perfect fluid of ordinary matter, together with a self-interacting scalar field fluid accounting for the dark energy in the universe. A priori assumptions about the functional form of the self-interaction potential or about the scale factor behavior are not neccessary. These are obtained as outputs of the assumed linear relationship between the Hubble expansion parameter a…
We study higher derivative corrections to black brane thermodynamics and their implications for the weak gravity conjecture for $p$-form gauge fields. In particular we show that higher derivative corrections decrease tension-to-charge ratios of extremal black branes as implied by the weak gravity conjecture, if four-derivative couplings follow scattering positivity bounds. We also demonstrate that entropy corrections in the micro canonical ensemble are positive under the same assumptions. This extends earlier works in the Einstein-Maxwell theory to $p$-form gauge fields in general spacetime di…
The emergent mechanism provides a possible way to resolve the big bang singularity problem by assuming that our universe originates from the Einstein static (ES) state. Thus, the existence of a stable ES solution becomes a very crucial prerequisite for the emergent scenario. In this paper, we study the stability of an ES universe in gravity theory with a non-minimal coupling between the kinetic term of a scalar field and the Einstein tensor. We find that the ES solution is stable under both scalar and tensor perturbations when the model parameters satisfy certain conditions, which indicates th…
We study the inflation scenario with the non-minimally derivative coupling $XR^{(3)}$, where $X=\nabla_μϕ\nabla^μϕ$, $ϕ$ is the inflaton and $R^{(3)}$ is the 3-dimensional intrinsic Ricci scalar on the spacelike hypersurface, and analytically calculate the corrections of $XR^{(3)}$ on the power spectra of primordial perturbations. It is found that for the $ϕ^2$ inflation model, the corresponding predictions can be driven to the best-fit region of the $n_s$-$r$ diagram.
Entropy is a fundamental concept from Thermodynamics and it can be used to study models on context of Creation Cold Dark Matter (CCDM). From conditions on the first ($\dot{S}\geq0$)\footnote{Throughout the present work we will use dots to indicate time derivatives and dashes to indicate derivatives with respect to scale factor.} and second order ($\ddot{S}<0$) time derivatives of total entropy in the initial expansion of Sitter through the radiation and matter eras until the end of Sitter expansion, it is possible to estimate the intervals of parameters. The total entropy ($S_{t}$) is calculat…
We promote the Immirzi parameter to be a minimally coupled scalar field and we analyzed the Hamiltonian constraints in the framework of Loop Quantum Gravity without the time gauge. Proper SU(2) connections can be defined and a term containing derivatives of the field $β$ enters into their definition. Furthermore, boost degrees of freedom are non-dynamical, while the super-momentum constraints coincide with the scalar field case. Hence, the kinematical Hilbert space can be defined as for gravity in presence of a minimally coupled scalar field. Then, we analyzed the dynamical implications of thi…
We consider diffeomorphism invariant theories of gravity with arbitrary higher derivative terms in the Lagrangian as corrections to the leading two derivative theory of Einstein's general relativity. We construct a proof of the zeroth law of black hole thermodynamics in such theories. We assume that a stationary black hole solution in an arbitrary higher derivative theory can be obtained by starting with the corresponding stationary solution in general relativity and correcting it order by order in a perturbative expansion in the coupling constants of the higher derivative Lagrangian. We prove…
One of the striking features of general relativity is that the Einstein equation is implied by the Clausius relation imposed on a small patch of locally constructed causal horizon. Extension of this thermodynamic derivation of the field equation to more general theories of gravity has been attempted many times in the last two decades. In particular, equations of motion for minimally coupled higher curvature theories of gravity, but without the derivatives of curvature, have previously been derived using a thermodynamic reasoning. In that derivation the horizon slices were endowed with an entro…
The present study is motivated by the study of reference [1], where the generalized second law of thermodynamics has been investigated for a flat FRW universe for two viable models of $f(T)$ gravity. In the present work, we have considered a non-flat universe and accordingly studied the behaviors of equation of state parameter and deceleration parameter. Subsequently, using the first law of thermodynamics we derived the expressions for the time derivative of the total entropy of a universe enveloped by apparent horizon. In the next phase, with the choice of scale factor pertaining to an emerge…
We investigate five-dimensional static (non-)extremal black hole solutions in higher derivative Anti-de Sitter gravity theories with neutral scalars non-minimally coupled to gauge fields. We explicitly identify the boundary counterterms to regularize the gravitational action and the stress tensor. We illustrate these results by applying the method of holographic renormalization to computing thermodynamical properties in several concrete examples. We also construct numerical extremal black hole solutions and discuss the attractor mechanism by using the entropy function formalism.
We explore thermodynamic properties of a new class of Horndeski black holes whose action contains a non-minimal kinetic coupling of a massless real scalar and the Einstein tensor. Our treatment is based on the well-accepted consideration, where the cosmological constant is dealt with as thermodynamic pressure and the mass of black holes as thermodynamic enthalpy. We resort to a newly introduced intensive thermodynamic variable, i.e., the coupling strength of the scalar and tensor whose dimension is length square, and thus yield both the generalized first law of thermodynamics and the generaliz…
We derive a simple form for the propagator of a massless, minimally coupled scalar in a locally de Sitter geometry of arbitrary spacetime dimension. We then employ it to compute the fully renormalized stress tensor at one and two loop orders for a massless, minimally coupled phi^4 theory which is released in Bunch-Davies vacuum at t=0 in co-moving coordinates. In this system the uncertainty principle elevates the scalar above the minimum of its potential, resulting in a phase of super-acceleration. With the non-derivative self-interaction the scalar's breaking of de Sitter invariance becomes o…
We show that effective theories of matter that classically violate the null energy condition cannot be minimally coupled to Einstein gravity without being inconsistent with both string theory and black hole thermodynamics. We argue however that they could still be either non-minimally coupled or coupled to higher-curvature theories of gravity.
Higher order derivative theories, generally suffer from instabilities, known as Ostrogradsky instabilities. This issue can be resolved by removing any existing degeneracy present in such theories. We consider a model involving at most second order derivatives of scalar field non-minimally coupled to curvature terms. Here we perform (3+1) decomposition of Lagrangian to separate second order time derivative form the rest. This is useful to check the degeneracy hidden in the Lagrangian will help us to find conditions under which Ostrogradsky instability do not appear. In our case, we find no such…
The present study is aimed at investigating the validity of the generalized second law (GSL) of thermodynamics in $f(\cal R)$ gravity. Choosing $f(\cal R)=R+ξR^μ+ζR^{-ν}$ [following Phys Rev D, 68, 123512 (2003)] we have computed the time derivatives of total entropy for various choices of scale factor pertaining to emergent, intermediate and logamediate scenarios of the universe. We have taken into account the radii of hubble, apparent, particle and event horizons while computing the time derivatives of entropy under various situations being considered. After analyzing through the plots of ti…
We give a complete description of the asymptotic behavior of a Friedmann-Robertson-Walker Universe with ``normal'' matter and a minimally coupled scalar field. We classify the conditions under which the Universe is or is not accelerating. In particular, we show that only two types of large time behavior exist: an exponential regime, and a subexponential expansion with the logarithmic derivative of the scale factor tending to zero. In the case of the subexponetial expansion the Universe accelerates when the scalar field energy density is dominant and the potential behaves in a specified manner,…
In arXiv:1508.01343 [hep-th], one of the authors proposed that in AdS/CFT the gravity dual of the boundary $c$-theorem is the second law of thermodynamics satisfied by causal horizons in AdS and this was verified for Einstein gravity in the bulk. In this paper we verify this for higher derivative theories. We pick up theories for which an entropy expression satisfying the second law exists and show that the entropy density evaluated on the causal horizon in a RG flow geometry is a holographic c-function. We also prove that given a theory of gravity described by a local covariant action in the …
We obtain topological black hole solutions in scalar-tensor gravity with nonminimal derivative coupling between scalar and tensor components of gravity and power-law Maxwell field minimally coupled to gravity. The obtained solutions can be treated as a generalization of previously derived charged solutions with standard Maxwell action \cite{Feng_PRD16}. We examine the behaviour of obtained metric functions for some asymptotic values of distance and coupling. To obtain information about singularities of the metrics we calculate Kretschmann scalar. We also examine the behaviour of gauge potentia…
