### Our (quantum and gravitating) physical universe from a conservative (neither compulsory stringy nor mandatory supersymmetric) viewpoint

**Welcome to observationally driven quantum cosmological times!**

The Planck measurements have unambiguously confirmed the main predictions of the theory of quantum origin of the universe structure. Namely, the adiabatic nature and the Gaussian origin of primordial perturbations were established beyond any reasonable doubt. Even more amazing, more nontrivial infrared logarithmic tilt of the spectrum, first predicted in [2], was discovered at 6 sigma confidence level. The simplest way to amplify the quantum fluctuations is provided by the stage of inflation. Although nobody doubt the quantum origin of the primordial fluctuations, there are still claims in the literature that basically the same mechanism of amplification of quantum fluctuations can work also either in a bouncing universe on the stage of super slow contraction [18] or in conformal rolling scenario [19]. The generated spectra in the alternative theories are not the predictions of the theory, but rather postdictions which are constructed to be in agreement with observations. Nevertheless, this is not enough to rule out these possibilities at the level of a ”theorem”. Thus,at the moment the only robustly established experimental fact is the quantum origin of the universe structure with a little uncertainty left for the mechanism of amplification of quantum fluctuations. To firmly establish that namely inflation has provided us this mechanism one has to find the primordial gravitational waves the lower bound on which for the spectral index ns= 0.96 corresponds to r about 0.003.

Inflation without Selfreproduction

Viatcheslav Mukhanov

(Submitted on 8 Sep 2014)

**Farewell to some plagues of postmodern inflating speculations?**

Production of a closed universe does not cost any energy because the positive energy of the matter is entirely compensated by the negative energy of the gravitational self-interaction of this matter. Therefore the closed universe can be produced as a result of quantum ﬂuctuations[7]. One can expect that quantum ﬂuctuations are essential only at Planck scale and only quantum universes with internal mass of order 10−5g can easily emerge. If gravity is an attractive force then such universes will immediately recollapse. However, as it was pointed out in [8],[9],[10], this does not happen if for some reason the equation of state within the Planckian universe corresponds to the cosmological constant p ≈−ε, where p is the pressure and ε is the energy density. In this case the gravitational ﬁeld, determined by ε+ 3p ≈−2ε, is repulsive and instead of collapsing the universe starts to expand with acceleration. As a result the size of the closed universe grows exponentially and its total mass (as well as the number degrees of freedom) also increases exponentially fast.The energy needed to produce the matter comes from the gravitational reservoir with unbounded from below energy. This is a rough picture of the emergence of the causal universe in Minkowski space [8] or from nothing [9],[10]1, which was proposed in 80th. This picture is also well supported by quantization of space-time in noncommutative geometry [11].The stage of accelerated expansion is useful for amplifying quantum ﬂuctuations which later serve as the seeds for galaxy formation [1], [2] and, moreover, it also ampliﬁes the quantum ﬂuctuations of transverse degrees of freedom of the gravitational ﬁeld (gravitational waves) [12].

There are many inﬂationary scenarios in the literature the only purpose of which is to provide us with the stage of the quasi-exponential expansion. These scenarios mainly differ by the choice of a slow-roll scalar ﬁeld potential “justiﬁed” by a “fundamental theory”. However such theory is not yet known and hence any particular potential is merely based on the prejudices of the authors.I believe that under such circumstances the more plausible approach is an effective description of inﬂation in terms of the effective equation of state1+p/ε=1+w(N)parametrized by the number of e-folds left until the end of inﬂation N.As it was shown in [13] even the simplest choice for the equation of state allows us to cover nearly all scenarios and to prove that the most valuable predictions of the theory of quantum origin of the universe structure are robust. [...]

If we want to avoid the selfreproduction and do not face the problem of initial conditions the required equation of state must simultaneously satisfy the following requirements:

1 + w(N) ≃ 1 at N ≃ 1 (to have graceful exit),1 + w (N) ≤ 2/3 at N ≃ Nm (to solve initial condition problem),1 + w (N) ≪ 1 for 1 < N < Nm (inﬂation),1 + w (N) > ε(N) for 1 < N < Nm (no selfreproduction).

Id.

//work in progress.

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