Modified Gravity Approaches to the Cosmological Constant Problem

Abstract

The cosmological constant and its phenomenology remain among the greatest puzzles in theoretical physics. We review how modifications of Einstein’s general relativity could alleviate the different problems associated with it that result from the interplay of classical gravity and quantum field theory. We introduce a modern and concise language to describe the problems associated with its phenomenology, and inspect no-go theorems and their loopholes to motivate the approaches discussed here. Constrained gravity approaches exploit minimal departures from general relativity; massive gravity introduces mass to the graviton; Horndeski theories lead to the breaking of translational invariance of the vacuum; and models with extra dimensions change the symmetries of the vacuum. We also review screening mechanisms that have to be present in some of these theories if they aim to recover the success of general relativity on small scales as well. Finally, we summarize the statuses of these models in their attempts to solve the different cosmological constant problems while being able to account for current astrophysical and cosmological observations.

Tadpole cosmology: self tuning without degeneracy

“…The field equations for this system are given in (17)(18)(19). Searching for a more general set of solutions beyond Milne, we expand a(τ ) and ϕ(τ ) around τ = 0 as…”

“…To go beyond the τ ≃ 0 expansion, we must numerically evolve the equations. In this section we evolve equations (17,18) for a range of scalar field initial conditions, solving the Friedmann equation ( 19) at some initial time and then using it as a consistency check that the dynamical equations are being correctly solved at each subsequent time-step. We fix λ = 1 and define all time and mass scales with respect to this choice.…”

“…However, the extreme discrepancy between the energy scale that is measured ρ vac ∼ O(10 −48 GeV 4 ) and what is naively expected ρ vac ∼ O(GeV 4 ) has led to a search for models that can naturally realise low energy vacuum states without fine tuning the vacuum energy. The problem is one of the most well-studied in the cosmology and high energy physics communities [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Attempts to tackle the problem typically involve renormalization, extra dimensions, quantum gravity corrections, unimodular gravity and more exotic approaches.…”

“…FIG.1. Numerical solutions to(17),(18), and(19) provided branch I initial conditions ((27) and (28)) with λ = 1, Λ = 10 −2 λ 4 , and ϕ0 = −xΛ/λ 3 where x is a randomly chosen in the range −10 −3 ≤ x ≤ 10 3 . The thick solid black line corresponds to x = 1; i.e.…”

“…FIG.3. Phase space representation of the numerical solutions to(17),(18), and (19) provided [left] branch I ((27) and (28)) and [right] branch II ((29) and (30)) initial states with λ = 1, Λ = 10 −2 λ 4 , and ϕ0 = −xΛ/λ 3 where x is a randomly chosen in the range −10 −3 ≤ x ≤ 10 3 . For the branch I solutions, the thick solid black line corresponds to x = 1; i.e.…”