Mori-Zwanzig formalism for early cosmic inflation

TL;DR

This work addresses how memory effects, encoded through a memory-dependent equation of state (MDES), can influence early-universe dynamics and drive inflation. By marrying Buchert averaging with the Mori-Zwanzig projection formalism, the authors derive nonlocal, history-dependent pressure terms that modify the Friedmann equations and yield an inflationary phase in the high-energy-density regime. They obtain closed-form expressions for the Hubble parameter and inflationary observables (e.g., $n_s$, $n_t$, $r$, $\alpha_s$) in terms of model parameters and show regions of agreement with Planck, BK18, BAO, and ACT data, while also outlining conditions from energy considerations. The results offer a robust, thermodynamics-inspired route to inflation and point to rich avenues for memory-enabled extensions, including stochastic inflation and memory-driven scalar fields, with potential implications for both early- and late-time cosmology.

Abstract

The existence of fluctuations at the early stage of the universe provides enough confidence to rely on averaging methods. However, the nonlinearity of general relativity makes this process extremely difficult. Several methods have been proposed to study inhomogeneous cosmology and address the averaging problem, such as Buchert's spatial averaging. In this work, early cosmic inflation is investigated using the Buchert equations and the Mori-Zwanzig projection operator formalism. The coarse-grained description derived from these approaches acts as a geometrical source of early cosmic inflation through higher-order differential equations. The theoretical results, while not an exact match, exhibit close agreement with observational data, demonstrating the robustness of the model and its potential for further cosmological applications.

Figures (15)

• Figure 1: This figure illustrates the regions where the NEC is satisfied and violated. It is based on the condition in Eq. \ref{['wdckwkefoei']} for the values $\zeta=-0.04$ and $\kappa=0.3$. The NEC is satisfied in the green area and violated in the red area.
• Figure 3: This figure illustrates the regions where the SEC is satisfied or violated. It is generated based on the conditions in Eqs. \ref{['dkjjwdbw']} and \ref{['dkjwjdkw']} for $\zeta=-0.04$ and $\kappa=0.3$. The red region indicates where both conditions are violated, the pink region corresponds to the violation of Eq. \ref{['dkjwjdkw']} while Eq. \ref{['dkjjwdbw']} is satisfied. The green region represents where both conditions hold.
• Figure 4: This plot illustrates the behavior of pressure in Eq. \ref{['wedj2edwei']}. At small time values, the pressure is negative, while at large time values, it becomes positive.
• Figure 5: This plot illustrates the behavior of the pressure equation \ref{['ddfwdfwdf']}. It shows that the pressure remains negative for all time values, decreases to zero at early times, and increases at later times.
• Figure 6: This plot depicts the behavior of the energy density given by Eq. \ref{['dfnedfninfe']}, showing that it remains positive for all time values, decreases to zero at early times, and increases at later times.