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

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 considered constant with value in a range, 0≤c<1. The NMDC effect is considered either as modification in kinetic scalar field or in gravitational constant. The NMDC effect allows gravitational constant to be time-varying. Since the NMDC effect is cosmological, definition of holographic density should include time-varying part of the gravitational constant. The NMDC part reduces strength of gravitational constant for κ>0 and opposite for κ<0. The holographic part enhances gravitational strength. Slow-roll parameters are derived. 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≥60. Power-law scalar potentials, V=V0ϕn with n=2,4, and exponential potential, V=V0exp(−βϕ) are considered. Combined parametric plots of κ and ϕ 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, Ġ/G|t0≲3×10−12year−1 (Zhao et al., 2018) which, for this model, results in 10−12year−1≳−κϕ̇ϕ̈/MP2. Positive κ is favored and greater c2 results in lifting up lower bound of κ.