Cosmological Constant as a Finite Temperature Effect

Abstract

The cosmological constant problem is examined by taking an Einstein--scalar with a Higgs-type potential and scrutinizing the infrared structure induced by finite temperature effects. A variant optimal perturbation theory is implemented in the recently proposed quantum-gravitational framework. The optimized renormalized mass, i.e., the renormalized mass determined by the variant optimal perturbation theory, of the scalar field turns out to be on the order of the temperature. This shifts the cosmological constant problem to compatibility of the consequent perturbative analysis. The compatibility is guaranteed essentially by renormalization group invariance of physical quantities. We point out the resummation behind the invariance.

Quantization of Gravity and Finite Temperature Effects

“…Although quantum gravitational effects (reviews of various approaches to quantization of a matter-gravity system can be found, e.g., in [1][2][3][4][5]) are often set aside, it has become increasingly clear through a series of recent works [6][7][8][9][10][11][12][13][14][15][16][17][18][19] that they are crucial for solving some of the outstanding problems in theoretical and astro-theoretical physics. For instance, they have proven to be indispensable for precisely formulating (and potentially solving) the black hole information paradox [6][7][8]20].…”

“…Quantized gravity ought also to be an optimal arena for a systematic formulation (and resolution) of the cosmological constant problem (see, e.g., [25][26][27] for reviews of the problem), since the resolution would require renormalization of the vacuum energy. A systematic analysis of vacuum energy has recently been conducted in a quantized gravity setup with finite-temperature [9]. In the present work we provide a brief review of some of these developments, and press on.…”

“…As an application of our quantization approach, we have recently tackled [9] the cosmological constant (CC) problem. Here we extend the one-loop analysis therein to twoloop.…”

“…Once temperature enters one deals with three different scales: the renormalized mass, the artificial energy scale introduced in dimensional regularization, and the temperature scale. As reviewed in [9], convergence of perturbation theory dictates that these scales be on the same orders of magnitudes as one another. We show that there exists an optimal perturbation theory (OPT) [60] procedure that quantitatively enforces this qualitative requirement.…”

“…In Section 3.2, we extend it to a finite-temperature setup. With the quantized metric contribution understood in [9], we focus on flat space analysis of a real Higgs-type scalar system in a flat background. We recap two-loop effective potential computation in the refined background field method.…”