No abstract

In a very recent paper [1], we have proposed a novel 4-dimensional gravitational theory with two dynamical degrees of freedom, which serves as a consistent realization of D→4 Einstein-Gauss-Bonnet gravity with the rescaled Gauss-Bonnet coupling constant ̃α. This has been made possible by breaking a part of diffeomorphism invariance, and thus is consistent with the Lovelock theorem. In the present paper, we study cosmological implications of the theory in the presence of a perfect fluid and clarify the similarities and differences between the results obtained from the consistent 4-dimensional theory and those from the previously considered, naive (and inconsistent) D→ 4 limit. Studying the linear perturbations, we explicitly show that the theory only has tensorial gravitational degrees of freedom (besides the matter degree) and that for 0̃α> and 0Ḣ<, perturbations are free of any pathologies so that we can implement the setup to construct early and/or late time cosmological models. Interestingly, a k4 term appears in the dispersion relation of tensor modes which plays significant roles at small scales and makes the theory different than not only general relativity but also many other modified gravity theories as well as the naive (and inconsistent) D→ 4 limit. Taking into account the k4 term, the observational constraint on the propagation of gravitational waves yields the bound ̃α ≲ 𝒪(1) eV−2. This is the first bound on the only parameter (besides the Newton's constant and the choice of a constraint that stems from a temporal gauge fixing) in the consistent theory of D→ 4 Einstein-Gauss-Bonnet gravity.

We study cosmological perturbations in mimetic matter scenario with a general higher derivative function. We calculate the quadratic action and show that both the kinetic term and the gradient term have the wrong sings. We perform the analysis in both comoving and Newtonian gauges and confirm that the Hamiltonians and the associated instabilities are consistent with each other in both gauges. The existence of instabilities is independent of the specific form of higher derivative function which generates gradients for mimetic field perturbations. It is verified that the ghost instability in mimetic perturbations is not associated with the higher derivative instabilities such as the Ostrogradsky ghost. * firouz@ipm.ir † gorji@ipm.ir ‡ shosseini@shahroodut.ac.ir, shossein@ipm.ir

1 We use the metric signature convention (−, +, +, +). 2 We work in natural unit in which M Pl = 1 where M Pl is the reduced Planck mass.

Existence of minimal length is suggested in any quantum theory of gravity such as string theory, double special relativity and black hole physics. One way to impose minimal length is deforming Heisenberg algebra in phase space which is called Generalized Uncertainty Principle (GUP). In this paper, we develop statistical mechanics in GUP framework. Our method is quite general and does not need to fix the generalized coordinates and momenta. We define general transformation in phase space which transforms usual Heisenberg algebra to a deformed one. In this method, quantum gravity effects only acts on the structure of phase space and we relate these effects to the density of states. We find an interesting phenomenon in Maxwell-Boltzmann statistics which has not a classical analogy. We show that there is an upper bound for the number of excited particles in the limit of high temperature which implies to the condensation. Also we study modification of Bose-Einstein condensation and the completely degenerate gas.