Inflation driven by Einstein-Gauss-Bonnet gravity

Abstract

We have explicitly demonstrated that scalar coupled Gauss-Bonnet gravity in four dimension can have non-trivial effects on the early inflationary stage of our universe. In particular, we have shown that the scalar coupled Gauss-Bonnet term alone is capable of driving the inflationary stages of the universe without incorporating slow roll approximation, while remaining compatible with the current observations. Subsequently, to avoid the instability of the tensor perturbation modes we have introduced a self-interacting potential for the inflaton field and have shown that in this context as well it is possible to have inflationary scenario. Moreover it turns out that presence of the Gauss-Bonnet term is incompatible with the slow roll approximation and hence one must work with the field equations in the most general context. Finally, we have shown that the scalar coupled Gauss-Bonnet term attains smaller and smaller values as the universe exits from inflation. Thus at the end of the inflation the universe makes a smooth transition to Einstein Therefore most of the inflationary paradigms are driven by a scalar field with a non-trivial self-interacting potential in Einstein gravity.A natural pathway through which such a scalar field can enter the gravitational dynamics at the early universe is through the coupling of the field with the Gauss-Bonnet term. The Gauss-Bonnet term is the first non-trivial higher curvature correction to the Einstein-Hilbert action [27][28][29][30], leading to second order field equations and hence avoiding the Ostrogradsky instability [31]. Even though the Gauss-Bonnet term alone, in the context of four dimensional physics, does not contribute to the gravitational field equations, the scalar coupling makes the Gauss-Bonnet term (and hence the field equations) non-trivial. Some aspects of this scalar coupled Gauss-Bonnet gravity in the context of early universe physics has been explored in [32][33][34][35][36][37][38][39][40][41][42][43] (for a set of earlier works in other alternative theories in the similar spirit, see ). Below we provide a brief discussion on the results obtained in these works.The inflationary paradigm has been explored in [36,37] only in the context of scalar coupled Gauss-Bonnet gravity, excluding the Einstein term. While in [39,43], even though the Einstein term was essential, the self-interacting potential itself governs the inflation, having no effect of the Gauss-Bonnet term. On the other hand, in [32][33][34][35] both the self-interacting potential as well as the Gauss-Bonnet coupling for the inflaton field has been considered, but in the context of slow-roll approximation (see also [35,[40][41][42]98,99]). Thus non-trivial effects of the scalar coupled Gauss-Bonnet term in the Einstein-Hilbert action, in absence of self-interacting scalar potential in the context of inflationary paradigm has not been explored before. Besides, even when the self-interacting potential is added to the action, the relevant consequences of not incorporating the slow-roll approximation...

Thermal rectification optimization in nanoporous Si using Monte Carlo simulations

“…where λpp is the average phonon mean-free-path (MFP) of Si. In previous work simulations were carried out to compare and validate the simulator for bulk values of silicon thermal conductivity [24,26,41,43]. In particular we have also shown that our simulator results compare very well with several literature simulation and experimental results for the thermal conductivity versus temperature for pristine bulk Si and porous Si cases [25,26].…”

“…This section gives details about the Monte Carlo approach we employ, its validation, and the assumptions related the scattering term used. Full details can be found in our previous works [24,41] . The simulation process is as follows: The simulation domain of size Lx = 1000 nm × Ly = 500 nm is initialized with a 'Hot' and 'Cold' end, set at TH = 310 K and TC = 290 K respectively.…”

“…3 We compute the thermal conductivity in the materials by solving the phonon Boltzmann transport equation using the Monte Carlo method as we described in our previous works [24][25][26]. The Monte Carlo (MC) approach offers great flexibility of geometrical configurations and parametric control over the scattering mechanisms that the phonons undergo, while still allowing very good accuracy [24,26] and large micrometer size simulation domains. Further details on the Monte Carlo simulation approach we employ and the assumptions made therein can be found in the Appendix.…”

“…All phonons reflect on the pores, with the pore boundaries taken to scatter all incident phonons in a specular fashion [24]. While systems with asymmetric roughness do have a thermal rectification effect [27], in this work we leave the effect of roughness aside, and focus on the geometrical configurations of the pores.…”

Bouncing cosmology in an extended theory of gravity

“…In bouncing cosmologies there is an initial phase of contraction where matter dominates the universe followed by a bounce without any singularity and then there is a causal generation for fluctuation. Bouncing cosmologies have been investigated in alternative gravity theories such as f (R) theory [31][32][33][34][35], modified Gauss-Bonnet gravity [36,37], f (R, T ) gravity [17] and f (T ) gravity [38].…”