Research Statement

My main research interest lies at the interface between Cosmology and Particle Physics. I have also worked on certain aspects of Chiral Phase Transition in relativistic heavy-ion collisions. In what follows, I give a brief description of the work done and directions of future research. References below correspond to the list of publications/preprints given in my CV.
 
 

A New Mechanism of Topological Defect Production

One of the exciting topics in the context of early universe is the formation of Topological Defects. These are exotic objects like Domain Walls, Cosmic Strings, Monopoles and Textures which are believed to have been formed during Phase Transitions in the very early universe. Topological Defects such as Cosmic Strings and Textures could have played a very important role in structure formation in the early Universe; on the other hand, topological defects such as monopoles which are believed to be produced in copious amounts during GUT phase transitions, are in conflict with observation and some mechanism such as inflation must be invoked to get rid of these defects. Cosmic strings have also been used to generate the observed baryon asymmetry of the Universe in certain models of Baryogenesis. In view of their important cosmological consequences, it is necessary to understand the various mechanisms by which these defects can be formed.

The main thrust of my work on Topological Defects has focussed on exploring the various mechanisms of formation of defects. In particular, we have demonstrated a new mechanism of formation of topological defects in which strong amplitude oscillations of the order-parameter(OP) field play a crucial role [1,2].

During first order phase transitions, occurring via bubble nucleation, when two or more bubbles collide, the bubble-wall energy is dissipated in the form of both magnitude and phase oscillations of the OP field. We have studied this process of bubble collisions and subsequent OP field dynamics through numerical simulations of a Global U(1) theory. When the bubbles collide, a vortex-antivortex (V-AV) pair is formed whenever the OP field ``flips'' through zero and crosses over to the opposite side of the vacuum manifold, during the course of strong magnitude oscillations brought about by the dissipation of wall energy. By analyzing in detail the results of our simulations, we are able to identify the conditions necessary for the ``flipping'' of the OP field and subsequent formation of V-AV pairs. These are strong magnitude oscillations of the OP field in a region of spatially varying phase.

These pairs supplement the defects formed via the conventional (Kibble) mechanism. This mechanism of defect formation is very dynamical and crucially depends on the energetics of the OP field.This is unlike the Kibble mechanism which depends only on the topology of the vacuum manifold and the dimension of space. We have shown that this mechanism is quite general and is applicable for the formation of topological defects such as monopoles and textures. We also find that for low bubble nucleation rates, this mechanism may completely dominate over the Kibble mechanism [2]. This may have important consequences for models of extended inflation.

We have shown that in systems in which the symmetry is explicitly as well as spontaneously broken, this mechanism can not only dominate over Kibble mechanism, but might be the only mechanism for defect formation [3]. The latter scenario is encountered when Kibble defects are completely suppressed because of the bias in the distribution of phases inside the bubbles arising from explicit symmetry breaking.
 
 

Resonant Production of Topological Defects

Normally topological defect formation is associated with phase transitions. However we have demonstrated a novel phenomenon [5] in which topological defects can form even without a phase transition. We study a system described by a spontaneously broken Global U(1) theory where the OP field is driven by a periodically varying (with time) effective potential. We consider the periodic variation of the effective potential to arise from the periodic variation of the temperature of the system. (This is however not essential and any uniform periodically varying field, inflaton for example, coupled to the OP field will do). We find that even for temperatures much below the critical temperature, resonant oscillations of the OP field (for a certain range of frequencies), lead to flipping of the field and consequent continued production of a large number of vortex-antivortex pairs via the flipping mechanism discussed in [1,2]. We discuss the similarities and differences of this mechanism of defect production with those discussed in the context of inflationary (p)reheating (Tkachev et.al. [PLB 440 (1998) 262]; Parry and Sornborger [PRD 60 (1999) 103504]; Kasuya and Kawasaki [PRD 58 (1998) 083516]). A crucial distinction between our work and those in the existing literature is the following. In the latter case, defects are produced due to non-thermal symmetry restoration and its subsequent breaking. However, in our case, there is no symmetry restoration ever and defects are produced due to localized "flipping" of the OP field.
 

Work in Progress/Future Research : As suggested above, such resonant production of defects, without any symmetry restoration, may have very important consequences in the post-inflationary reheating scenarios. In such scenarios, the quasi-periodically oscillating inflaton field coupled to a complex scalar field with broken U(1) symmetry can act as a driver for the latter, and may induce resonant oscillations leading to defect production. This will lead to additional contribution to the overall defect density and may ultimately affect the evolution of the universe. Even monopoles can form if the system has the appropriate vacuum manifold with non-trivial second Homotopy group. If resonant oscillations of the OP field lead to copious monopole-antimonopole production, this will lead to severe constraints on many inflationary models. I am currently studying the possibility of resonant defect production without any symmetry restoration (either thermal or non-thermal) in the context of realistic inflationary models taking into account the effect of expansion of the universe.

Another interesting extension of the above work would be to study the effect of noise on resonant defect production in Condensed Matter Physics. An interesting phenomenon known as Stochastic Resonance is observed in several periodically driven systems subject to white noise; for example, a particle in a double-well potential trapped in one of the wells and under the influence of a periodically varying (with time) driving force and white noise. I will be investigating the possibility of defect production due to resonance enhancement because of the noise term and study the effects of tuning the noise strength on the defect density. Moreover in the work discussed above, there is an upper cut-off for the dissipation coefficient beyond which resonant production of defects are not observed. This means that in condensed matter systems, most of which are overdamped, such resonant production of defects will not be observed. However, the addition of noise and periodic driving may make it possible even for such systems to produce defects by the resonant oscillations of the OP field. This is another problem that I will be exploring.
 
 

Disoriented Chiral Condensates (DCC)

Domains of Disoriented Chiral Condensates may form during a Chiral Phase Transition in relativistic heavy ion collisions. All the works on formation of DCC have focussed on the possibility of formation of DCC domains starting with a chirally symmetric state at a temperature T_i > T_c. The subsequent cooling (due to expansion) of the plasma is taken to give rise to a quench-like scenario. The resulting out-of-equilibrium evolution of the chiral fields can lead to exponential growth of long-wavelength fluctuations. If such exponential growth occurs over a sufficiently long time scale, it can lead to the establishment of large correlations implying formation of large domains of DCC. The subsequent decay of these DCC's would then lead to strong fluctuations in charged to neutral pion ratio (as in Centauro events observed in Cosmic Ray experiments). Detection of this effect will provide a signature of the chiral phase transition.

I have worked on the possibility of Large DCC formation in which the initial state for evolution of the chiral field was different from that of the earlier works on DCC [4]. There we explore the possibility of disorienting the chiral field due to rapid change in effective potential during the early stages of plasma evolution[4]. We start from a state in which the chiral field is in the true vacuum($f_{\pi},0$) everywhere just after heavy-ion collision and just before the whole system starts equilibrating due to interactions to a temperature T_i. We then show that if the heating is rapid enough then the chiral field can overshoot to the opposite point on the vacuum manifold, thereby disorienting the vacuum. This happens due to driving of the chiral field by the rapidly changing effective potential. We investigate the field dynamics by studying the trajectories of the mean field (obtained by averaging over an appropriate volume) subject to dissipation and white noise, using a Langevin equation (as was also done by Biro and Greiner [PRL 79 (1997) 3138]). We then obtain the probability of forming an (approximately coherent) large DCC domain.
 

Work in Progress/Future Research : In the above work, the spatial variation of the field was not taken into account which means that we had ignored the effects of domain-domain coupling on the evolution of the chiral field. I am currently studying the effects of taking into account the spatial variation of the chiral field by carrying out a 3D Langevin simulation of the Linear Sigma Model, subject to white noise and dissipation. An important thing to check here is the effects of non-trivial topology of the chiral field configuration on pion distributions for which we had given qualitative arguments in the work described above. I want to check the predictions regarding this by carrying out a 3D Langevin simulation and make quantitative predictions about the resulting pion distribution.

An exciting possibility which I plan to explore is that of Pattern Formation during a Chiral Phase Transition. In a recent paper by Sornborger and Parry [PRL 83 (1999) 666] the authors studied pattern formation in the context of post-inflationary preheating scenarios where driven dissipative systems exist. They showed that a self-coupled scalar field (the inflaton) quasi-periodically oscillating in its potential can exhibit pattern formation. Such driven dissipative systems also exist during a chiral phase transition when the chiral field starts oscillating about the true vacuum. Oscillations of the sigma field about the true vacuum provide the driving force and situations similar to that of preheating scenarios after inflation exist even during a chiral phase transition. In fact in an interesting paper, Kaiser [PRD 59 (1999) 117901] exploited the similarity between field dynamics in post-inflationary preheating scenarios and field dynamics during a chiral phase transition to show that large domain of DCC can form due to parametric resonance effects when the sigma field starts oscillating about the true vacuum. In view of the above discussions, its clear that driven, dissipative systems similar to those found in post-inflationary scenarios of preheating can exist during a chiral phase transitions and hence there is a distinct possibility of such systems exhibiting pattern formation as well.
 
 

Electroweak Baryogenesis

In a recent work I have explored the possibility of Baryogenesis occurring due to Hawking radiation emitted by primordial black holes embedded in a universe whose ambient temperature is much below the Electroweak transition temperature [6]. The Hawking radiation emitted by the black holes can heat up the surrounding plasma to temperatures above the electroweak transition temperatures, thereby leading to the restoration of electroweak symmetry locally. The plasma cools as it moves due to diffusion or pressure gradients and electroweak baryogenesis can occur in the regions where temperature drops below the EW transition temperature. (Similar results have also been obtained recently by Nagatani [PRD 59 (1999) 041301].)

An interesting aspect of our model is that adequate baryon asymmetry can be produced even if the EW phase transition is of second order. Also, in our model, there is no constraint on the Higgs mass since the ambient temperature of the universe is much below the electroweak scale resulting in suppressed sphaleron transitions.
 

Work in Progress/Future Research : We are planning to carry out a more thorough analysis of the process of heating up of the plasma by the primordial black holes, thereby making more definitive predictions. Also we are planning to explore the possibility of production of topological defects due to local heating of the plasma by the black holes.
 

Curriculum  Vitae

 

 

    This  page  was  created  using   LaTeX2HTML

    Last  Updated  on  5.12.99