I read big bang theory of universe creation, but I want to know the Vedic concept of universe creation and in how much time it is created?
In this answer I will not be quoting the exact verses initially, however I will be providing the links wherein you can read.
The Vedic concept of creation includes the "HOW" and the "WHY" of the entire cosmic manifestation.
What was there before creation?
Supreme personality of godhead, Lord Krishna who is beyond material creation exists before creation and after annihilation. Period after annihilation and before creation all living entities are dormant in the form of the Lord. [SB 3.5.23]
Reason for creation
The compassion of the Lord towards living entities: Lord is mercifully putting so much endeavour from His side to reclaim conditioned beings, creating universe, residing as supersoul in heart to guide and sanction jiva’s desires, maintaining and winding the universe, sending acharyas to reclaim fallen souls and so on. [SB 3.5.3]
The Lord felt incomplete without His plenary expansions and unsatisfied, so he desired to create the manifestation. The material potency was dormant. [SB 3.5.24]
CREATION IN BRIEF (From Srimad Bhagavatam)
janma sarga udahrtah
visargah paurusah smrtah
The elementary creation of sixteen items of matter—namely the five elements [fire, water, land, air and sky], sound, form, taste, smell, touch, and the eyes, ears, nose, tongue, skin and mind—is known as sarga, whereas subsequent resultant interaction of the modes of material nature is called visarga.
atmanah saha saktibhih
muktir hitvanyatha rupam
The merging of the living entity, along with his conditional living tendency, with the mystic lying down of the Maha-Visnu is called the winding up of the cosmic manifestation. Liberation is the permanent situation of the form of the living entity after he gives up the changeable gross and subtle material bodies.
puruso ’ndam vinirbhidya
yadasau sa vinirgatah
atmano ’yanam anvicchann
apo ’sraksic chucih sucih
After separating the different universes, the gigantic universal form of the Lord [Maha-Visnu], which came out of the causal ocean, the place of appearance for the first purusa-avatara, entered into each of the separate universes, desiring to lie on the created transcendental water [Garbhodaka].
antah sarira akasat
ojah saho balam jajne
tatah prano mahan asuh
From the sky situated within the transcendental body of the manifesting Maha-Visnu, sense energy, mental force and bodily strength are all generated, as well as the sum total of the fountainhead of the total living force.
pranenaksipata ksut trd
antara jayate vibhoh
pipasato jaksatas ca
pran mukham nirabhidyata
The living force, being agitated by the virat-purusa, generated hunger and thirst, and when He desired to drink and eat, the mouth opened.
mukhatas talu nirbhinnam
tato nana-raso jajne
jihvaya yo ’dhigamyate
From the mouth the palate became manifested, and thereupon the tongue was also generated. After this all the different tastes came into existence so that the tongue can relish them.
vivaksor mukhato bhumno
vahnir vag vyahrtam tayoh
jale caitasya suciram
When the Supreme desired to speak, speeches were vibrated from the mouth. Then the controlling deity Fire was generated from the mouth. But when He was lying in the water, all these functions remained suspended.
tatra vayur gandha-vaho
ghrano nasi jighrksatah
Thereafter, when the supreme purusa desired to smell odors, the nostrils and respiration were generated, the nasal instrument and odors came into existence, and the controlling deity of air, carrying smell, also became manifested.
atmanam ca didrksatah
nirbhinne hy aksini tasya
jyotis caksur guna-grahah
Thus when everything existed in darkness, the Lord desired to see Himself and all that was created. Then the eyes, the illuminating god Sun, the power of vision and the object of sight all became manifested.
jighrksatas tvan nirbhinna
tatra cantar bahir vatas
tvaca labdha-guno vrtah
When there was a desire to perceive the physical characteristics of matter, such as softness, hardness, warmth, cold, lightness and heaviness, the background of sensation, the skin, the skin pores, the hairs on the body and their controlling deities (the trees) were generated. Within and outside the skin is a covering of air through which sense perception became prominent.
gatim jigisatah padau
padbhyam yajnah svayam havyam
karmabhih kriyate nrbhih
Thereupon, because of His desiring to control movement, His legs became manifested, and from the legs the controlling deity named Visnu was generated. By His personal supervision of this act, all varieties of human being are busily engaged in dutiful occupational sacrifice.
nirabhidyata sisno vai
upastha asit kamanam
Thereupon, for sexual pleasure, begetting offspring and tasting heavenly nectar, the Lord developed the genitals, and thus there is the genital organ and its controlling deity, the Prajapati. The object of sexual pleasure and the controlling deity are under the control of the genitals of the Lord.
nirabhidyata vai gudam
tatah payus tato mitra
Thereafter, when He desired to evacuate the refuse of eatables, the evacuating hole, anus, and the sensory organ thereof developed along with the controlling deity Mitra. The sensory organ and the evacuating substance are both under the shelter of the controlling deity.
asisrpsoh purah purya
tatrapanas tato mrtyuh
Thereafter, when He desired to move from one body to another, the navel and the air of departure and death were combinedly created. The navel is the shelter for both, namely death and the separating force.
nadyah samudras ca tayos
tustih pustis tad-asraye
When there was a desire to have food and drink, the abdomen and the intestines and also the arteries became manifested. The rivers and seas are the source of their sustenance and metabolism.
tato manas candra iti
sankalpah kama eva ca
When there was a desire to think about the activities of His own energy, then the heart (the seat of the mind), the mind, the moon, determination and all desire became manifested.
The seven elements of the body, namely the thin layer on the skin, the skin itself, the flesh, blood, fat, marrow and bone, are all made of earth, water and fire, whereas the life breath is produced by the sky, water and air.
The sense organs are attached to the modes of material nature, and the modes of material nature are products of the false ego. The mind is subjected to all kinds of material experiences (happiness and distress), and the intelligence is the feature of the mind’s deliberation.
etad bhagavato rupam
sthulam te vyahrtam maya
astabhir bahir avrtam
Thus by all this, the external feature of the Personality of Godhead is covered by gross forms such as those of planets, which were explained to you by me.
atah param suksmatamam
nityam van-manasah param
Therefore beyond this [gross manifestation] is a transcendental manifestation finer than the finest form. It has no beginning, no intermediate stage and no end; therefore it is beyond the limits of expression or mental speculation and is distinct from the material conception.
sattvam rajas tama iti
tatrapy ekaikaso rajan
bhidyante gatayas tridha
According to the different modes of material nature—the mode of goodness, the mode of passion and the mode of darkness—there are different living creatures, who are known as demigods, human beings and hellish living entities. O King, even a particular mode of nature, being mixed with the other two, is divided into three, and thus each kind of living creature is influenced by the other modes and acquires its habits also.