Recently, it has been proposed by Padmanabhan that the difference between the number of degrees of freedom on the boundary surface and the number of degrees of freedom in a bulk region leads to the expansion of the universe. Now, a natural question arises; how could this model explain the oscillation of the universe between contraction and expansion branches? We try to address this issue in the framework of a BIonic system. In this model, M0-branes join to each other and give rise to a pair of M1-anti-M1-branes. The fields which live on these branes play the roles of massive gravitons that cause the emergence of a wormhole between them and formation of a BIon system. This wormhole dissolves into M1-branes and causes a divergence between the number of degrees of freedom on the boundary surface of M1 and the bulk leading to an expansion of M1-branes. When M1-branes become close to each other, the square energy of their system becomes negative and some tachyonic states emerge. To remove these states, M1-branes become compact, the sign of compacted gravity changes, causing anti-gravity to arise: in this case, branes get away from each other. By articulating M1-BIons, an M3-brane and an anti-M3-brane are created and connected by three wormholes forming an M3-BIon. This new system behaves like the initial system and by closing branes to each other, they become compact and, by getting away from each other, they open. Our universe is located on one of these M3-branes and, by compactifying the M3-brane, it contracts and, by opening it, it expands. a

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Recently, some authors removed the big-bang singularity and predicted an infinite age of our universe. In this paper, we show that the same result can be obtained in string theory and M-theory; however, the shape of universe changes in different epochs. In our mechanism, first, N fundamental string decay to N D0-anti-D0-brane. Then, D0-branes join to each other, grow and and form a six-dimensional brane-antibrane system. This system is unstable, broken and present form of four dimensional universes , one anti-universe in additional to one wormhole are produced. Thus, there isn't any big-bang in cosmology and universe is a fundamental string at the beginning. Also, total age of universe contains two parts, one in related to initial age and second which is corresponded to present age of universe (ttot = t initial + tpresent). On the other hand, initial age of universe includes two parts, the age of fundamental string and time of transition (t initial = ttransition + t f −string ). We observe that only in the case of (t f −string → ∞), the scale factor of universe is zero and as a result, total age of universe is infinity.PACS numbers: 98.80.-k, 04.50.Gh, 11.25.Yb, 98.80.Qc I. INTRODUCTIONRecently, some authors obtained the second order Friedmann equations from the quantum corrected Raychaudhuri equation (QRE), and argued that these equations include two quantum correction terms, the first of which can be interpreted as cosmological constant, while the second as a radiation term in the early universe, which gets rid of the big-bang singularity and predicts an infinite age of our universe [1]. In parallel, some models have been proposed to remove big-bang singularity in BIonic system [2][3][4][5]. In this system, at the beginning, there are k black fundamental strings that transited to the BIon configuration at an special energy. At this energy, two brane and antibrane universes are produced, interact with each other through a wormhole and inflate. This wormhole gives it's energy to the brane universes and causes to inflation. Shortly, the wormhole disappears, the inflation ends and a deceleration epoch begins. When the brane and antibrane universes become close together, a tachyon is produced, grows and leads the creation of a new wormhole. At this stage, this tachyonic wormhole connects the brane and antibrane universes again and leads to the late-time acceleration era of the universe [2,4]. Now, the main question arises as to what is the relation between the model which was obtained from QRE and the one which was used BIon? We will answer this question in this paper. We also modify previous discussions in BIon by introducing D0-branes and clarify transitions in this system. In our model, at the beginning, there are N fundamental strings that excited and make a transition to N D0-anti-D0-branes. Then, by joining and growing these objects, a pair of brane-antibrane is formed. These branes interact with each other, emit D0-branes and changes to lower dimensional branes like D3-branes. The present universe is located ...

Recently, Padmanabhan [arXiv:1206.4916 [hep-th]]discussed that the difference between the number of degrees of freedom on the boundary surface and the number of degrees of freedom in a bulk region causes to the accelerated expansion of the universe. The main question arises as to what is the origin of this inequality between the surface degrees of freedom and the bulk degrees of freedom? We answer this question in M-theory. In our model, first M0-branes are compactified on one circle and N D0-branes are created. Then, N D0-branes join to each other, grow and form one D5-branes. Next, D5-brane is compactified on two circle and our universe-D3-brane, two D1-brane and some extra energies are produced. After that, one of D1-branes which is more close to universe-brane, gives it's energy into it, leads to an increase in difference between number of degrees of freedom and occurring inflation era. With the disappearance of this D1-brane, the number of degrees of freedom of boundary surface and bulk region become equal and inflation ends. At this stage, extra energies that are produced due to the compactification cause to an expansion of universe and deceleration epoch. Finally, another D1-brane, dissolves in our universe-brane , leads to an inequality between degrees of freedom and happening a new phase of acceleration.