A simple harmonic universe

Abstract

We explore simple but novel bouncing solutions of general relativity that avoid singularities. These solutions require curvature k = +1, and are supported by a negative cosmological term and matter with −1 < w < −1/3. In the case of moderate bounces (where the ratio of the maximal scale factor a + to the minimal scale factor a − is O(1)), the solutions are shown to be classically stable and cycle through an infinite set of bounces. For more extreme cases with large a + /a − , the solutions can still oscillate many times before classical instabilities take them out of the regime of validity of our approximations. In this regime, quantum particle production also leads eventually to a departure from the realm of validity of semiclassical general relativity, likely yielding a singular crunch. We briefly discuss possible applications of these models to realistic cosmology.

Tunneling decay rate in quantum cosmology

“…Oscillating cosmological models have been extensively studied over the years (see, e.g., [1,2] and references therein). Such models can be classically stable with respect to small perturbations [2][3][4], but it was pointed out in [5,6] that they are generically unstable with respect to decay through quantum tunneling to zero size.…”

Did the Universe Have a Beginning?

“…With the Hamiltonian constraint H = 0, enforcing zero total energy of the universe, we recover the oscillating universe solutions discussed in [10]. We quantize the theory by letting the momentum become the differential operator p a → −i d da and replacing the Hamiltonian constraint with the WheelerDeWitt equation [15] Hψ = 0.…”

“…In the emergent universe model, the universe is closed and static in the asymptotic past (recent work includes [6,7,8,9,10]; for early work on oscillating models see [11]). Then H av = 0 and the incompleteness theorem [3] does not apply.…”

“…Graham et al [10] recently proposed a simple emergent model featuring a closed universe (k = +1) with a negative cosmological constant (Λ < 0) and a matter source which obeys P = wρ, where −1 < w < −1/3. Graham et al point out that the matter source should not be a perfect fluid, since this would lead to instability from short-wavelength perturbations [10].…”

“…Graham et al point out that the matter source should not be a perfect fluid, since this would lead to instability from short-wavelength perturbations [10]. One such material that fulfills this requirement is a network of domain walls, which has w = −2/3.…”