Sstrhsrtj

It is said that Veda was one and later Vyasa arranged it into four ( rig sama yaju atharva) and then propagated through his pupil and hence we got shakhaas etc.

What was time when vedas were rearranged into four?

Were it only one before that?

I am looking for authentic reference for vedas becoming four from one and the era when it was done.

According to Devi Bhagavatam too Veda Vyasa divides the Veda into four parts in Dwapara Yuga of each Manvantara.

18-24. At every Manvantara, in each Dvâpara Yuga, Veda Vyâsa expounds
the Purânas duly to preserve the religion. Veda Vyâsa is no other
person than Visnu Himself; He, in the form of Veda Vyâsa, divides the
(one) Veda into four parts, in every Dvâpara Yuga, for the good of the
world. The Brahmânas of the Kali age are shortlived and their
intellect (Buddhi) is not sharp; they cannot realise the meaning after
studying the Vedas; knowing this in every Dvâpara Yuga Bhagavân
expounds the holy Purâna Samhitas.

From the Purana's Book 1, Chapter 3

We find a clear reference in Srimad Bhagavatam 1.4.19 that Bhagavan Veda Vyasa divided the Vedas from one into four.

He saw that the sacrifices mentioned in the Vedas were means by which the people’s occupations could be purified. And to simplify the process he divided the one Veda into four, in order to expand them among men.

Regarding when this was done Srimad Bhagavatam 1.4.25 has the answer again. It was done prior to compiling the Mahabharata, which means in the Dwapara Yuga before Kali Yuga since the sequence is mentioned in the verses.

Out of compassion, the great sage thought it wise that this would enable men to achieve the ultimate goal of life. Thus he compiled the great historical narration called the Mahābhārata for women, laborers and friends of the twice-born.

We also find in Srimad Bhagavatam 12.6.50,

Śrīla Vyāsadeva separated the mantras of the Ṛg, Atharva, Yajur and Sāma Vedas into four divisions, just as one sorts out a mixed collection of jewels into piles. Thus he composed four distinct Vedic literatures.

Q. When?
A. At the end of Dwaparayuga

Q. By Whom?
A. By VedaVyasa

Q. Why?
A. Considering shortened strength and life-time (incapability to learn whole Veda) in Kaliyuga

Q. How?
A. According to Mantras used in Yajna by Ritvij

According to Srimad Bhagavatam 12.6:

Vedas are manifested from OMkara:

Text 40-41

One perceives this [eternal, itself imperceptibly manifesting] sound, outside the physical sense of hearing and power of vision. The complete of the Vedic sound one employs is an elaboration of this omkâra that from the soul manifests itself in the ether. It constitutes the direct expression of the self-generating Absolute Truth and Supersoul, it constitutes the eternal seed of the Vedas and constitutes the secret of all mantras [see also 7.15: 31, 9.14: 48, 11.14: 34-35, 11.21: 36-40].
Vedas inherently constitutes Rik, Yajur and Sama hymns (even before the division):

Which inherently constitutes Rik, Sama and Yajur (even before the division of Vedas)

Text 42

Oh eminence of Bhrigu, the three sounds of the alphabet beginning with A that came into being [the sounds A, U and M], are fundamental to [all] the threefold forms of material existence: the modes [the gunas], the names [of the three Vedas], the destinations [the three types of lokas] and the states of consciousness [avasthâtraya].

Brahma manifested four Vedas from his four faces:

Text 44

For the purpose of giving instruction on the four sacrifices [see ritvik], the almighty one created with all these sounds from his four faces the four Vedas, along with his omkâra and vyâhriti invocations [of the names of the seven lokas].

Brahma taught Vedas to his son as one (complete set - without division):

Text 45

He taught them [as a complete set] to his sons who were the great rishis among the brahmins most expert in the art of Vedic recitation, and they in their turn imparted them as instructors of dharma [âcâryas] to their sons.

Touching the question:

These headed down in in every Yugas upto Dwapara and divided at the end of Dwaparayuga:

ते परम्परया प्राप्तास्तत्तच्छिष्यैर्धृतव्रतैः ।

चतुर्युगेष्वथ व्यस्ता द्वापरादौ महर्षिभिः ॥ ४६॥

Text 46

Throughout the four yugas generation after generation, one after the other disciple fixed in his vows received them [these Vedas] by disciplic succession [paramparâ]. They were divided among the prominent sages at the end of Dvâpara-yuga.

The reason for division is incapability and short life-period of man near to Kaliyuga: (as I mentioned in this answer)

Text 47

The brahmin sages, inspired by the Infallible Lord situated in their hearts, came to that dividing among each other of the Vedas when they saw that under the influence of time the intelligence [of the people] diminished, the life span shortened and the strength weakened [see also 1.4: 16-18].

Observing that under the influence of kâla [the people became] lesser intelligent and short-lived and that their strength was diminished, divided the chief sages, inspired by the Infallible Lord situated in their hearts, the Vedas [see also 1.4: 16-18].

The one who has accomplished the task of division (in present Manavantara) is none other than Vyasa:

Text 48-49
Oh brahmin, in this period [of Manu], Brahmâ and S'iva and other rulers over the worlds requested the Supreme Lord, the Protector of the Universe, to protect the principles of religion. Oh most fortunate soul, the Lord [in the form of Krishna Dvaipâyana Vyâsa], by Parâs'ara begotten in the womb of Satyavatî, then descended as a partial expansion of His plenary portion [Sankarshana] and divided the Veda in four.

How Vyasa divided Vedas (as I discussed in this answer) is explained in further verse:

Text 50

Like someone sorting out gems, he separated the group of mantras in four categories of collections [Samhitâs]: the Rig, Atharva, Yajur and Sâma Veda [see Vedas].

In the Vayu Purana [60.16–18] Suta Gosvami explains:

itihasa-purananam vaktaram samyag eva hi mam caiva pratijagraha
bhagavan ishvarah prabhuh eka asid yajur-vedas tam caturdha
vyakalpayat caturhotram abhut tasmims tena yajnam akalpayat
adhvaryavam yajurbhis tu rigbhir hotram tathaiva ca audgatram
samabhish caiva brahmatvam capy atharvabhih

“Shrila Vyasadeva, the almighty Supreme Lord, accepted me [Suta
Gosvami] as the qualified speaker of the Itihasas and Puranas. In the
beginning there was only one Veda, the Yajur Veda, which Shrila Vyasa
divided into four parts. These gave rise to the four activities called
catur-hotra, by means of which Shrila Vyasa arranged for the
performance of sacrifice.
The adhvaryu priests carry out their responsibilities with
yajur-mantras, the hota priests with rig-mantras, the udgata priests
with sama-mantras, and the brahma priests with atharva-mantras.”

According to Vishnu Purana[3.3.9–10]:

ashöavimshati kritva vai/ veda vyasta maharshibhih vaivasvate 'ntare
hy asmin/ dvapareshu punah punah veda-vyasa vyatita ye/ ashöavimshati
sattama caturdha yaih krito vedo/ dvapareshu punah punah

"During this period of Vaivasvata Manu's reign, already twenty eight
different exalted sages have edited the Vedas in one Dvapara age after
another. Twenty eight Veda-vyasas have already come and gone, O best
of souls, dividing the Veda into four parts in each Dvapara-yuga"

Vayaviya Samhita of Shiva purana states[7.1.1.37–38]:

sankshipya caturo vedamsh caturdha vyabhajat prabhuh vyasta-vedataya
khyato veda-vyasa iti smritah puranam api sankshiptam
catur-laksha-pramanatah adyapy amartya-loke tu shata-koöi-pravistaram

“The ingenious Lord abridged the Veda and then divided it [vyasta]
into four. Therefore He became known as Veda-vyasa. He also summarized
the Puranas in four hundred thousand verses, but in the heavenly
planets they still comprise one billion verses”

Shri Vishnu Purana states [3.4.2.–5]

tato ’tra mat-suto vyasa ashöavimshatime ’ntare vedam ekam
catush-padam caturdha vyabhajat prabhuh yathatra tena vai vyasta
veda-vyasena dhi-mata vedas tatha samastais tair vyasair anyais tatha
maya tad anenaiva vyasanam shakha-bhedan dvijottama catur-yugeshu
racitan samasteshv avadharaya krishna-dvaipayanam vyasam viddhi
narayanam prabhum ko ’nyo hi bhuvi maitreya mahabharata-krid bhavet

"Thereafter, during the twenty-eighth manv-antara, the Lord in the
form of my son Vyasa took the one Veda, consisting of four sections,
and divided it into four separate parts. Just as this intelligent
Vyasa divided the Veda, previously all other Vyasas, including myself,
also divided it. O best of the twice-born, understand that in every
cycle of four yugas Vyasas come and arrange the Veda into various
branches. But know, O Maitreya, that Shri Krishna-dvaipayana Vyasa is
Lord Narayana Himself. Who else in this world could have written the
great epic Mahabharata?”

Kurma Purana (52.19–20), Vyasadeva’s followers further divided the four Vedas into 1,130 branches:

eka-vimshati-bhedena rig-vedam kritavan pura shakhanam tu shatenaiva
yajur-vedam athakarot sama-vedam sahasrena shakhanam prabibheda sah
atharvanam atho vedam bibheda navakena tu

“Formerly the Rig Veda was divided into 21 branches, the Yajur Veda
into 100 branches, the Sama Veda into 1,000 branches, and the Atharva
Veda into 9 branches.”