Emergence of multiverse in third quantized varying constants cosmologies

Abstract

Although the standard cosmological model explains most of the observed phenomena it still struggles with the problem of initial singularity. An interesting scenario in which the problem of the initial singularity is somehow circumvented was proposed in the context of string theory where the canonical quantisation procedure was additionally applied [2]. A similar effect can be achieved in the context of the canonically quantized theory with varying speed of light and varying gravitational constant where both quantities are represented by non-minimally coupled scalar fields [4]. Such theory contains both the prebig-bang contracting phase and the post-big-bang expanding phase and predicts non-vanishing probability of the transition from the former to the latter phase. In this paper we quantize such a theory once again by applying the third quantization scheme and show that the resulting theory contains scenario in which the whole multiverse is created from nothing. The generated family of the universes is described by the Bose-Einstein distribution.

Doubleverse entanglement in third quantized non-minimally coupled varying constants cosmologies

“…We have shown that the canonical quantization of the Wheeler-DeWitt wave function for non-minimally coupled varying constants model introduced in [13] results in a theory which comprises a scenario that describes the two quantum mechanically entangled -one expanding and one contracting -branches. This is different form the scenario developed in [12] where the third quantization applied to the same model led to a scenario in which a whole multiverse subjected to Bose-Einstein distribution emerged form nothing. The discrepancy in these two scenarios follows form different interpretations of the representation dependent sets of vectors spanning the Hilbert space resulting form the third quantization procedure assumed in both approaches.…”

“…The discrepancy in these two scenarios follows form different interpretations of the representation dependent sets of vectors spanning the Hilbert space resulting form the third quantization procedure assumed in both approaches. In scenario given in [12] the orthonormal basis that generates the Hilbert space of the multiverse is assumed to represent an occupation with universes in a given state while in the scenario considered in the present paper the basis that spans the Hilbert space is assumed to represent an excitation levels of one of the two systems which naturally leads to entanglement in a pair of single universes that form the doubleverse (compare with approaches introduced in [7][8][9][19][20][21]). Such an approach also facilitates a description of the entanglement in terms of quantities which are formal analogs [10] of the ordinary thermodynamical quantities such as the entropy, the internal energy, heat and work.…”

“…Our considerations are based on the model defined in [12,13] which describes the variation of the speed of light and the variation of the gravitational constant with both quantities represented by the two non-minimally coupled scalar fields. Such a model was originally inspired by the covariant and locally Lorentz-invariant varying speed of light theories [17] and is given by the following action:…”

“…The formula (13) encodes the typical impact of varying speed of light on classical trajectories due to explicit dependence of the metric on the speed of light c (see [17]). Inserting (10) and (11) into (12) and then integrating (12) leads to the following relation between x 0 and the rescaled cosmic timex 0 [13]:…”

“…Many different cosmological scenarios have been considered so far in the context of the third quantization. We mention here an embedding of Brans-Dicke gravity in the third quantization scheme which interestingly leads to scenarios in which whole multiverse is created out of vacuum [11], an application of third quantization procedure to the varying constants model [12] with non-minimally coupled dynamical scalar fields representing the speed of light and the gravitational constant [13] which results in similar scenario of the multiverse creation or eventually the third quantization of the varying gravitational constant cyclic scenarios [14] in which the naturally arisen interuniversal entanglement leads to interesting behavior of the thermodynamical quantities [9]. The third quantization procedure was also used to discuss the transition from expanding to contracting cosmological phase (and vice-versa) in [15,16].…”