Quantum entanglement versus inflation in the early universe Quantum entanglement is one of the most fascinating and mysterious phenomena in nature. It needs no interactions, or any sort of exchange for it to take place. It is possible, not against any rules of physics as far as we know, that all matter that was created in the early universe was in an entangled state. 
The question is:
Is it possible to explain the uniformity and isotropy of matter in the universe, by means of quantum entanglement in the early 'days' of universe? If that could be possible, would it mean that there would be no need for the inflationary model any more?
If this problem has been researched in detail, any references posted will be appreciated.
 A: I've found this paper: Cosmological quantum entanglement, of E. Martin-Martinez and N. C. Menicucci.
(last revised 19 Oct. 2012)

Abstract     We review recent literature on the connection between quantum entanglement and cosmology, with an emphasis on the context of
expanding universes. We discuss recent theoretical results reporting
on the production of entanglement in quantum fields due to the
expansion of the underlying spacetime. We explore how these results
are affected by the statistics of the field (bosonic or fermionic),
the type of expansion (de Sitter or asymptotically stationary), and
the coupling to spacetime curvature (conformal or minimal). We then
consider the extraction of entanglement from a quantum field by
coupling to local detectors and how this procedure can be used to
distinguish curvature from heating by their entanglement signature. We
review the role played by quantum fluctuations in the early universe
in nucleating the formation of galaxies and other cosmic structures
through their conversion into classical density anisotropies during
and after inflation. We report on current literature attempting to
account for this transition in a rigorous way and discuss the
importance of entanglement and decoherence in this process. We
conclude with some prospects for further theoretical and experimental
research in this area. These include extensions of current theoretical
efforts, possible future observational pursuits, and experimental
analogues that emulate these cosmic effects in a laboratory setting.

More recently (14 Aug. 2014): Entanglement in curved spacetimes and cosmology, of the same authors.

Abstract We review recent results regarding entanglement in quantum fields in cosmological spacetimes and related phenomena in
flat spacetime such as the Unruh effect. We being with a summary of
important results about field entanglement and the mathematics of
Bogoliubov transformations that is very often used to describe it. We
then discuss the Unruh-DeWitt detector model, which is a useful model
of a generic local particle detector. This detector model has been
successfully used as a tool to obtain many important results. In this
context we discuss two specific types of these detectors: a qubit and
a harmonic oscillator. The latter has recently been shown to have
important applications when one wants to probe nonperturbative physics
of detectors interacting with quantum fields. We then detail several
recent advances in the study and application of these ideas, including
echoes of the early universe, entanglement harvesting, and a nascent
proposal for quantum seismology.

A: Entanglement results when the system under consideration belongs to one quantum mechanical solution of the specific  problem.
The inflationary period as introduced at the beginning of the Big Bang model is a quantum mechanical solution to the boundary problem of the very early universe. At those sizes and energy densities  it is assumed that everything is described with a  quantum mechanical model. Specific models,  are used to check consistency with the cosmic background radiation and the density of galaxy clusters in the observable universe, more or less successfully.
The dominant quantum field theoretical  model presently  is the one with a scalar field :

According to inflation theory, the inflaton is a scalar field that is responsible for cosmic inflation in the very early universe. A quantized particle for this field is expected, similar to other quantum fields, called an inflaton. The field provides a mechanism by which a period of rapid expansion from 10−35 to 10−34 seconds after the initial expansion can be generated, forming the universe .

It is consistent with the observation.  The aim is to explain the observations and this quantum mechanical model  leads to inflation at the early universe, and the fields and particles it posits are by construction entangled.
It is possible that another quantum mechanical model might describe the homogeneity of the observations without leading to rapid inflation, but it would be by different fields and boundary assumptions;  entanglement will exist in any quantum mechanical model.
A: One of the problems that inflation solves is the so-called horizon problem. The problem is that parts of the sky that don't appear to have been in causal contact have the same temperature. Inflation solves this problem because before the period of rapid expansion all parts of the sky were in causal contact.
Let us consider whether entanglement - which is long-distance correlation - can help us correlate patches of the sky that have the same temperature but don't appear to have been in causal contact. Unfortunately, we encounter an obstacle:

In order for two subsystems to be in an entangled state, they must
have interacted (i.e. been in causal contact) in the past.

Without going through any detailed realization of your idea, I don't think it's going to get around the horizon problem. Entanglement couldn't explain how patches of the sky became entangled if they weren't in causal contact.
A: I have been contemplating this same phenomenon. It is true that quantum mechanics predominated in the early universe prior to first light and thus a significant amount of quantum entanglement must have existed. It has been shown, so far as I know of, that quantum entangled particles had to be in close communication at some point in the past, but it may be possible that if two or more disparate and identical particles assume the exact same quantum state then they may possible become entangled even if separated by vast distances in space and time. We are not far enough advanced in this field of research to totally rule out that possibility. If enough particles distributed across a wide enough volume of space time became entangled then that could result in a transfer of information (but not matter) at greater distances than the horizon limitation would normally allow. However the likelihood of that is very slim. The scalar field, and the inflationary period predicted by it, seems to be a much more likely candidate to describe the early Universe and the slight variations temperatures measured in the CBR.
A: Perhaps the entanglement in question is not that of the "usual" quantum fields, but rather entanglement of the elements of quantum space-time themselves.
Quantum tunneling of the entanglement energy in the bulk may have occurred as a result of the Big Crunch.
Since no coherent vacuum existed at the moment of the Big Bang, propagation of an entanglement field would not be limited to velocity c.
The inflaton field is then seen as an entanglement field, establishing the vacuum with its rigid Minkowski metric and high vacuum energy.
