Cosmology in holographic non-minimal derivative coupling theory: constraints from inflation and variation of gravitational constant

TL;DR

This paper explores a holographic non-minimal derivative coupling cosmological model, analyzing its inflationary predictions and constraints from gravitational constant variation, ultimately ruling out NMDC inflation within the considered parameter space.

Contribution

It introduces a holographic NMDC model with a time-varying gravitational constant and tests its inflationary predictions against CMB data, providing new insights into late-time dynamics and observational constraints.

Findings

NMDC inflation is ruled out for 0 < c < 1.

Holographic NMDC inflation is also ruled out for 0 < c < 1.

The model predicts new late-time attractor trajectories in acceleration regions.

Abstract

We consider a cosmological model of non-minimal derivative coupling (NMDC) to gravity with holographic effect from Bekenstein-Hawking entropy using Hubble horizon IR cutoff. Holographic parameter $c$ is constant in a range, $0 \leq c < 1$. NMDC effect allows gravitational constant to be time-varying. Definition of holographic density include time-varying part of the gravitational constant. NMDC part reduces strength of gravitational constant for $\k > 0$ and opposite for $\k < 0$. The holographic part enhances gravitational strength. We use spectral index and tensor-to-scalar ratio to test the model against CMB constraint. Number of e-folding is chosen to be $N \geq 60$. Potentials, $V = V_0 \phi^n $ with $n = 2, 4$, and $V = V_0 \exp{(-\beta \phi)}$ are considered. Combined parametric plots of $\k$ and $\phi$ show that the allowed regions of the power spectrum index and of the tensor-to-scalar ratio are not overlapping. NMDC inflation is ruled out and the holographic NMDC inflation is also ruled out for $0 < c < 1$. NMDC significantly changes major anatomy of the dynamics, i.e. it gives new late-time attractor trajectories in acceleration regions. The holographic part clearly affects pattern of trajectories. However, for the holographic part to affect shape of the acceleration region, the NMDC field must be in presence. To constrain the model at late time, variation of gravitational constant is considered. Gravitational-wave standard sirens and supernovae data give a constraint, $\dot{G}/G|_{t_0} \lesssim 3\times10^{-12} \, \text{year}^{-1}$ \cite{Zhao:2018gwk} which, for this model, results in $ 10^{-12} \, \text{year}^{-1} \, \gtrsim \, {- \kappa} \dot{\phi}\ddot{\phi}/{M^2_{\p}}\,. $ Positive $\k$ is favored and greater $c^2$ results in lifting up lower bound of $\k$.