Higgs Field in Universe: Long-Term Oscillation and Deceleration/Acceleration Phases

It is shown that the Einstein gravity and Higgs scalar field have (a) a long-term oscillation phase; (b) cosmological regular solutions with deceleration/acceleration phases. The first has a preceding contracting and subsequent expanding phases and between them there exists an oscillating phase with arbitrary time duration. The behavior of the second solution near to a flex point is in detail considered. 1. Introduction The standard cosmological model (for review, see [1]) gives us an accurate description of the evolution of the Universe. In spite of its success, the standard cosmological model has a series of problems such as the initial singularity, the cosmological horizon, the flatness problem, the baryon asymmetry, and the nature of dark matter and dark energy. Under the dynamical laws of general relativity, the standard FLRW cosmology becomes singular at the origin of Universe. The matter density and geometrical invariants diverge as the volume of the Universe goes to zero. The Big Bang singularity seems to be an unavoidable aspect of the currently established cosmological model [2] which probably only a full quantum theory of gravity could resolve. A bouncing Universe with an initial contraction to a nonvanishing minimal radius; then subsequently an expanding phase provides a possible solution to the singularity problem of the standard Big Bang cosmology. Bouncing cosmologies, in which the present era of expansion is preceded by a contracting phase, have been studied as potential alternatives to inflation in solving the problems of standard FRW cosmology. The first explicit semianalytic solution for a closed bouncing FRW model filled by a massive scalar field was found by Starobinskii [3]. Later explicit solutions for a bouncing geometry were obtained by Novello and Salim [4] and Melnikov and Orlov [5]. For the review of the cosmological bounce one can see review [6]. Supernova observations [7, 8] were the first to suggest that our Universe is currently accelerating. For this acceleration now it is believed that as much as 2/3 of the total density of the Universe is in a form which has large negative pressure and which is usually referred to as dark energy. A number of various models have been proposed aiming at the description of dark energy universe (for review, see [9–11]). It is evident that to have deceleration (where ) and acceleration (where ) phases it is necessary to have the moment with . Here we would like to show that (a) a Universe bounce can be not only a short time event but also it can be a long-term oscillating process; (b) the