Cosmic Acceleration as the Solution to the Cosmological Constant Problem

Abstract

In this paper we provide both a diagnosis and resolution of the cosmological constant problem, one in which a large (as opposed to a small) cosmological constant " can be made compatible with observation. We trace the origin of the cosmological constant problem to the assumption that the local gravi-tational Newton constant G (as measured in a Cavendish experiment) sets the scale for global cosmology. Then we show that once this assumption is relaxed, the very same cosmic acceleration that has served to make the cosmological constant problem so very severe can instead serve to provide us with its potential resolution. In particular, we present an alternate cosmology, one based on conformal gravity, a theory whose e †ective cosmological not only di †ers from the Cavendish one by being G eff altogether smaller than it but, by even being explicitly negative, naturally leads to cosmological repulsion. We show in the conformal theory that once given only that the sign of " is speciÐcally the negative one associated with spontaneous scale symmetry breaking, then that alone, no matter how big " might actually be in magnitude, is not only sufficient to make the actually measurable contribution of " to current era cosmology naturally be of order 1 today, but to even do so in a 8nG eff "/3cH2(t 0) way that is fully compatible with the recent high-z supernova cosmology data. Thus, to solve the cosmo-logical constant problem, we do not need to change or quench the energy content of the universe, but rather we only need to change its e †ect on cosmic evolution. Subject headings : cosmological parameters È cosmology : theory È gravitation 1. DIAGNOSIS OF THE COSMOLOGICAL CONSTANT PROBLEM The recent discovery by Riess et al. (1998) and Perlmutter et al. (1999) of a cosmic acceleration has made the already extremely disturbing cosmological constant problem even more vexing than before. SpeciÐcally, a phenomenological Ðtting to the new high-z supernova Hubble plot data using the standard Einstein-Friedmann cosmological evolution equations R0 2(t) ] kc2 \ R0 2(t)[) M (t) ]) " (t)] , (1)) M (t) ]) " (t) ]) k (t) \ 1 , (2) q(t) \ An 2 [ 1 B) M (t) [) " (t) , (3) where is due to ordinary matter) M (t) \ 8nGo M (t)/3c2H2(t) [viz., matter for which where A [ 0 and o M (t) \ A/Rn(t), 3 ¹ n ¹ 4], where is due to a cosmo-) " (t) \ 8nG"/3cH2(t) logical constant ", and where is due to) k (t) \ [kc2/R0 2(t) the spatial three-curvature k, has revealed that not only must the current era actually be nonzero today, it) " (t 0) is even explicitly required to be of order 1. Typically, the allowed parameter space compatible with the available data is found to be centered on the line or so) " (t 0) \) M (t 0) ] 1 2 with (the presumed positive) being found to be) M (t 0) limited to the range (0, 1) and to the range 3/2) or) " (t 0) (1 2 , so, with the current (n \ 3) era deceleration parameter thus having to approxi-q(t 0) \ (n/2 [ 1)) M (t 0) [) " (t 0) mately lie within the [1) interval.1 Thus, not only ([1 2 , do we Ðnd that the universe is currently accelerating, but additionally we see that with there being no allowed solution at all [unless could somehow be) " (t 0) \ 0) M (t 0) allowed to go negative], the long-standing problem (for some recent reviews see, e.g., Weinberg 1989 ; Ng 1992) of trying to Ðnd some way by which [and thus) " (t 0) q(t 0)] could be quenched by many orders of magnitude from its quantum gravity Planck temperature expectation or its typical K) particle physics expecta-c o " o \ pT V 4 (T V ^ 1016 tion has now been replaced by the need to Ðnd a speciÐc such mechanism that in practice (rather than just in principle) would explicitly put into this very narrow) " (t 0) 3/2) box. Not only is it not currently known how it might (1 2 , be possible to actually do this, up to now no mechanism has been identiÐed that might even Ðx the sign of the standard model let alone its magnitude.) " (t 0), Now while such quenching of " has yet to be achieved, it is important to note that even if it were to actually be achieved, the very use of such a quenched " in equation (1) 1 The spread around the line is of order thus) " (t 0) \) M (t 0) ] 1 2 ^1 2 , allowing solutions in which the current era is negligible, with) M (t 0)) " (t 0) having to then lie in the (0, 1) interval and in (0, [1) [for explicit q(t 0) acceptable Ðts in the "" empty universe ÏÏ case in which is) M (t 0) \ 0) " (t 0) also zero, see Dev, Sethi, & Lohiya 2000]. While completely foreign to the standard model, as we shall see below, universes where has little o M (t 0) e †ect on current era cosmic evolution can nonetheless actually occur quite naturally in the alternate conformal gravity theory that we explore in this paper.